## 25 Reputation

4 years, 297 days

## fix the solve problem pls...

Maple 18

restart;
Solve({(6*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2+12*alpha^2*k^2*lambda*v*a[1]-12*alpha^2*k^2*lambda*a[1]-3*k^2*lambda*v*a[1]+3*k^2*lambda*a[1]+(3*(8*alpha^2*k^2*v^2*a[1]-16*alpha^2*k^2*v*a[1]+8*alpha^2*k^2*a[1]-2*k^2*v^2*a[1]+4*k^2*v*a[1]-2*k^2*a[1]))*d = 0, (-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3)*d^6+(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2)*d^5+(-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-4*alpha^4*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]+beta*a[1])*d^4+(4*alpha^2*k^2*lambda*mu*a[1]-8*L*alpha^2*a[0]^3-48*L*alpha^2*a[0]*a[1]*a[2]-4*alpha^4*a[0]-k^2*lambda*mu*a[1]+2*L*a[0]^3+12*L*a[0]*a[1]*a[2]-4*alpha^2*beta*a[0]+alpha^2*a[0]-2*a[0]^3-12*a[0]*a[1]*a[2]+beta*a[0])*d^3+(-24*L*alpha^2*a[0]^2*a[2]-24*L*alpha^2*a[1]*a[2]^2-4*alpha^4*a[2]+6*L*a[0]^2*a[2]+6*L*a[1]*a[2]^2-4*alpha^2*beta*a[2]+alpha^2*a[2]-6*a[0]^2*a[2]-6*a[1]*a[2]^2+beta*a[2])*d^2+(-4*alpha^2*k^2*lambda*mu*a[2]-24*L*alpha^2*a[0]*a[2]^2+k^2*lambda*mu*a[2]+6*L*a[0]*a[2]^2-6*a[0]*a[2]^2)*d+8*alpha^2*k^2*mu^2*a[2]-2*a[2]^3-2*k^2*mu^2*a[2]-8*L*alpha^2*a[2]^3+2*L*a[2]^3 = 0, (6*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d^5+(5*(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2))*d^4+(4*(-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-4*alpha^4*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]+beta*a[1]))*d^3+(3*(4*alpha^2*k^2*lambda*mu*a[1]-8*L*alpha^2*a[0]^3-48*L*alpha^2*a[0]*a[1]*a[2]-4*alpha^4*a[0]-k^2*lambda*mu*a[1]+2*L*a[0]^3+12*L*a[0]*a[1]*a[2]-4*alpha^2*beta*a[0]+alpha^2*a[0]-2*a[0]^3-12*a[0]*a[1]*a[2]+beta*a[0]))*d^2+(4*alpha^2*k^2*lambda^2*a[1]+8*alpha^2*k^2*mu*v*a[1]-8*alpha^2*k^2*mu*a[1]-k^2*lambda^2*a[1]-2*k^2*mu*v*a[1]+2*k^2*mu*a[1])*d^3+(2*(-24*L*alpha^2*a[0]^2*a[2]-24*L*alpha^2*a[1]*a[2]^2-4*alpha^4*a[2]+6*L*a[0]^2*a[2]+6*L*a[1]*a[2]^2-4*alpha^2*beta*a[2]+alpha^2*a[2]-6*a[0]^2*a[2]-6*a[1]*a[2]^2+beta*a[2]))*d+12*alpha^2*k^2*lambda*mu*a[2]-24*L*alpha^2*a[0]*a[2]^2-3*k^2*lambda*mu*a[2]+6*L*a[0]*a[2]^2-6*a[0]*a[2]^2+(-4*alpha^2*k^2*lambda^2*a[2]-8*alpha^2*k^2*mu*v*a[2]+8*alpha^2*k^2*mu*a[2]+k^2*lambda^2*a[2]+2*k^2*mu*v*a[2]-2*k^2*mu*a[2])*d = 0, (15*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d^2+(5*(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2))*d+(3*(12*alpha^2*k^2*lambda*v*a[1]-12*alpha^2*k^2*lambda*a[1]-3*k^2*lambda*v*a[1]+3*k^2*lambda*a[1]))*d+(3*(8*alpha^2*k^2*v^2*a[1]-16*alpha^2*k^2*v*a[1]+8*alpha^2*k^2*a[1]-2*k^2*v^2*a[1]+4*k^2*v*a[1]-2*k^2*a[1]))*d^2+8*alpha^2*k^2*mu*v*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]-4*alpha^4*a[1]+4*alpha^2*k^2*lambda^2*a[1]-8*alpha^2*k^2*mu*a[1]-2*k^2*mu*v*a[1]-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-k^2*lambda^2*a[1]+2*k^2*mu*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]+beta*a[1] = 0, (15*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d^4+(10*(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2))*d^3+(6*(-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-4*alpha^4*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]+beta*a[1]))*d^2+(12*alpha^2*k^2*lambda*v*a[1]-12*alpha^2*k^2*lambda*a[1]-3*k^2*lambda*v*a[1]+3*k^2*lambda*a[1])*d^3+(3*(4*alpha^2*k^2*lambda*mu*a[1]-8*L*alpha^2*a[0]^3-48*L*alpha^2*a[0]*a[1]*a[2]-4*alpha^4*a[0]-k^2*lambda*mu*a[1]+2*L*a[0]^3+12*L*a[0]*a[1]*a[2]-4*alpha^2*beta*a[0]+alpha^2*a[0]-2*a[0]^3-12*a[0]*a[1]*a[2]+beta*a[0]))*d+(3*(4*alpha^2*k^2*lambda^2*a[1]+8*alpha^2*k^2*mu*v*a[1]-8*alpha^2*k^2*mu*a[1]-k^2*lambda^2*a[1]-2*k^2*mu*v*a[1]+2*k^2*mu*a[1]))*d^2+(-12*alpha^2*k^2*lambda*v*a[2]+12*alpha^2*k^2*lambda*a[2]+3*k^2*lambda*v*a[2]-3*k^2*lambda*a[2])*d+8*alpha^2*k^2*mu*v*a[2]-6*a[0]^2*a[2]-6*a[1]*a[2]^2-4*alpha^4*a[2]+4*alpha^2*k^2*lambda^2*a[2]-8*alpha^2*k^2*mu*a[2]-2*k^2*mu*v*a[2]-24*L*alpha^2*a[0]^2*a[2]-24*L*alpha^2*a[1]*a[2]^2-k^2*lambda^2*a[2]+2*k^2*mu*a[2]+6*L*a[0]^2*a[2]+6*L*a[1]*a[2]^2-4*alpha^2*beta*a[2]+alpha^2*a[2]+beta*a[2] = 0, (20*(-8*L*alpha^2*a[1]^3+2*L*a[1]^3-2*a[1]^3))*d^3+(10*(-24*L*alpha^2*a[0]*a[1]^2+6*L*a[0]*a[1]^2-6*a[0]*a[1]^2))*d^2+(4*(-24*L*alpha^2*a[0]^2*a[1]-24*L*alpha^2*a[1]^2*a[2]-4*alpha^4*a[1]+6*L*a[0]^2*a[1]+6*L*a[1]^2*a[2]-4*alpha^2*beta*a[1]+alpha^2*a[1]-6*a[0]^2*a[1]-6*a[1]^2*a[2]+beta*a[1]))*d+(8*alpha^2*k^2*v^2*a[1]-16*alpha^2*k^2*v*a[1]+8*alpha^2*k^2*a[1]-2*k^2*v^2*a[1]+4*k^2*v*a[1]-2*k^2*a[1])*d^3+(3*(4*alpha^2*k^2*lambda^2*a[1]+8*alpha^2*k^2*mu*v*a[1]-8*alpha^2*k^2*mu*a[1]-k^2*lambda^2*a[1]-2*k^2*mu*v*a[1]+2*k^2*mu*a[1]))*d+(3*(12*alpha^2*k^2*lambda*v*a[1]-12*alpha^2*k^2*lambda*a[1]-3*k^2*lambda*v*a[1]+3*k^2*lambda*a[1]))*d^2+(-8*alpha^2*k^2*v^2*a[2]+16*alpha^2*k^2*v*a[2]-8*alpha^2*k^2*a[2]+2*k^2*v^2*a[2]-4*k^2*v*a[2]+2*k^2*a[2])*d+4*alpha^2*k^2*lambda*v*a[2]+2*L*a[0]^3-4*alpha^4*a[0]-48*L*alpha^2*a[0]*a[1]*a[2]+4*alpha^2*k^2*lambda*mu*a[1]-4*alpha^2*k^2*lambda*a[2]-k^2*lambda*v*a[2]-k^2*lambda*mu*a[1]+12*L*a[0]*a[1]*a[2]+k^2*lambda*a[2]-8*L*alpha^2*a[0]^3-12*a[0]*a[1]*a[2]-4*alpha^2*beta*a[0]+alpha^2*a[0]+beta*a[0]-2*a[0]^3 = 0, 8*alpha^2*k^2*v^2*a[1]-8*L*alpha^2*a[1]^3-16*alpha^2*k^2*v*a[1]+8*alpha^2*k^2*a[1]-2*k^2*v^2*a[1]+2*L*a[1]^3+4*k^2*v*a[1]-2*k^2*a[1]-2*a[1]^3 = 0}, {alpha, a[0], a[1], a[2]});
/ /  /          2     3           3         3\
Solve|{ 6 \-8 L alpha  a[1]  + 2 L a[1]  - 2 a[1] / d
\ \

2          2                2              2
- 24 L alpha  a[0] a[1]  + 6 L a[0] a[1]  - 6 a[0] a[1]

2  2                         2  2
+ 12 alpha  k  lambda v a[1] - 12 alpha  k  lambda a[1]

2                    2                 /       2  2  2
- 3 k  lambda v a[1] + 3 k  lambda a[1] + 3 \8 alpha  k  v  a[

2  2                 2  2           2  2
1] - 16 alpha  k  v a[1] + 8 alpha  k  a[1] - 2 k  v  a[1]

2             2     \        /          2     3
+ 4 k  v a[1] - 2 k  a[1]/ d = 0, \-8 L alpha  a[1]

3         3\  6
+ 2 L a[1]  - 2 a[1] / d

/           2          2                2              2\  5
+ \-24 L alpha  a[0] a[1]  + 6 L a[0] a[1]  - 6 a[0] a[1] / d  +

/           2     2                  2     2
\-24 L alpha  a[0]  a[1] - 24 L alpha  a[1]  a[2]

4                2                2
- 4 alpha  a[1] + 6 L a[0]  a[1] + 6 L a[1]  a[2]

2                  2              2
- 4 alpha  beta a[1] + alpha  a[1] - 6 a[0]  a[1]

2                 \  4   /       2  2
- 6 a[1]  a[2] + beta a[1]/ d  + \4 alpha  k  lambda mu a[1]

2     3             2
- 8 L alpha  a[0]  - 48 L alpha  a[0] a[1] a[2]

4         2                          3
- 4 alpha  a[0] - k  lambda mu a[1] + 2 L a[0]

2                  2
+ 12 L a[0] a[1] a[2] - 4 alpha  beta a[0] + alpha  a[0]

3                                \  3   /
- 2 a[0]  - 12 a[0] a[1] a[2] + beta a[0]/ d  + \
2     2                  2          2          4
-24 L alpha  a[0]  a[2] - 24 L alpha  a[1] a[2]  - 4 alpha  a[2]

2                     2          2
+ 6 L a[0]  a[2] + 6 L a[1] a[2]  - 4 alpha  beta a[2]

2              2                   2            \  2
+ alpha  a[2] - 6 a[0]  a[2] - 6 a[1] a[2]  + beta a[2]/ d  +

/        2  2                            2          2
\-4 alpha  k  lambda mu a[2] - 24 L alpha  a[0] a[2]

2                               2              2\
+ k  lambda mu a[2] + 6 L a[0] a[2]  - 6 a[0] a[2] / d

2  2   2              3      2   2
+ 8 alpha  k  mu  a[2] - 2 a[2]  - 2 k  mu  a[2]

2     3           3        /          2     3
- 8 L alpha  a[2]  + 2 L a[2]  = 0, 6 \-8 L alpha  a[1]

3         3\  5
+ 2 L a[1]  - 2 a[1] / d

/           2          2                2              2\
+ 5 \-24 L alpha  a[0] a[1]  + 6 L a[0] a[1]  - 6 a[0] a[1] /

4     /           2     2                  2     2
d  + 4 \-24 L alpha  a[0]  a[1] - 24 L alpha  a[1]  a[2]

4                2                2
- 4 alpha  a[1] + 6 L a[0]  a[1] + 6 L a[1]  a[2]

2                  2              2
- 4 alpha  beta a[1] + alpha  a[1] - 6 a[0]  a[1]

2                 \  3     /       2  2
- 6 a[1]  a[2] + beta a[1]/ d  + 3 \4 alpha  k  lambda mu a[1]

2     3             2
- 8 L alpha  a[0]  - 48 L alpha  a[0] a[1] a[2]

4         2                          3
- 4 alpha  a[0] - k  lambda mu a[1] + 2 L a[0]

2                  2
+ 12 L a[0] a[1] a[2] - 4 alpha  beta a[0] + alpha  a[0]

3                                \  2   /       2  2
- 2 a[0]  - 12 a[0] a[1] a[2] + beta a[0]/ d  + \4 alpha  k

2               2  2                    2  2
lambda  a[1] + 8 alpha  k  mu v a[1] - 8 alpha  k  mu a[1]

2       2           2                2        \  3     /
- k  lambda  a[1] - 2 k  mu v a[1] + 2 k  mu a[1]/ d  + 2 \
2     2                  2          2          4
-24 L alpha  a[0]  a[2] - 24 L alpha  a[1] a[2]  - 4 alpha  a[2]

2                     2          2
+ 6 L a[0]  a[2] + 6 L a[1] a[2]  - 4 alpha  beta a[2]

2              2                   2            \
+ alpha  a[2] - 6 a[0]  a[2] - 6 a[1] a[2]  + beta a[2]/ d

2  2                            2          2
+ 12 alpha  k  lambda mu a[2] - 24 L alpha  a[0] a[2]

2                               2              2   /
- 3 k  lambda mu a[2] + 6 L a[0] a[2]  - 6 a[0] a[2]  + \
2  2       2               2  2
-4 alpha  k  lambda  a[2] - 8 alpha  k  mu v a[2]

2  2            2       2           2
+ 8 alpha  k  mu a[2] + k  lambda  a[2] + 2 k  mu v a[2]

2        \           /          2     3           3
- 2 k  mu a[2]/ d = 0, 15 \-8 L alpha  a[1]  + 2 L a[1]

3\  2
- 2 a[1] / d

/           2          2                2              2\
+ 5 \-24 L alpha  a[0] a[1]  + 6 L a[0] a[1]  - 6 a[0] a[1] / d + 3

/        2  2                         2  2
\12 alpha  k  lambda v a[1] - 12 alpha  k  lambda a[1]

2                    2            \       /       2  2  2
- 3 k  lambda v a[1] + 3 k  lambda a[1]/ d + 3 \8 alpha  k  v

2  2                 2  2           2  2
a[1] - 16 alpha  k  v a[1] + 8 alpha  k  a[1] - 2 k  v  a[1]

2             2     \  2          2  2
+ 4 k  v a[1] - 2 k  a[1]/ d  + 8 alpha  k  mu v a[1]

2              2               4
- 6 a[0]  a[1] - 6 a[1]  a[2] - 4 alpha  a[1]

2  2       2               2  2
+ 4 alpha  k  lambda  a[1] - 8 alpha  k  mu a[1]

2                       2     2
- 2 k  mu v a[1] - 24 L alpha  a[0]  a[1]

2     2         2       2           2
- 24 L alpha  a[1]  a[2] - k  lambda  a[1] + 2 k  mu a[1]

2                2               2
+ 6 L a[0]  a[1] + 6 L a[1]  a[2] - 4 alpha  beta a[1]

2                          /          2     3
+ alpha  a[1] + beta a[1] = 0, 20 \-8 L alpha  a[1]

3         3\  3
+ 2 L a[1]  - 2 a[1] / d

/           2          2                2              2\
+ 10 \-24 L alpha  a[0] a[1]  + 6 L a[0] a[1]  - 6 a[0] a[1] /

2     /           2     2                  2     2
d  + 4 \-24 L alpha  a[0]  a[1] - 24 L alpha  a[1]  a[2]

4                2                2
- 4 alpha  a[1] + 6 L a[0]  a[1] + 6 L a[1]  a[2]

2                  2              2
- 4 alpha  beta a[1] + alpha  a[1] - 6 a[0]  a[1]

2                 \     /       2  2  2
- 6 a[1]  a[2] + beta a[1]/ d + \8 alpha  k  v  a[1]

2  2                 2  2           2  2
- 16 alpha  k  v a[1] + 8 alpha  k  a[1] - 2 k  v  a[1]

2             2     \  3     /       2  2       2
+ 4 k  v a[1] - 2 k  a[1]/ d  + 3 \4 alpha  k  lambda  a[1]

2  2                    2  2
+ 8 alpha  k  mu v a[1] - 8 alpha  k  mu a[1]

2       2           2                2        \       /
- k  lambda  a[1] - 2 k  mu v a[1] + 2 k  mu a[1]/ d + 3 \12

2  2                         2  2
alpha  k  lambda v a[1] - 12 alpha  k  lambda a[1]

2                    2            \  2   /
- 3 k  lambda v a[1] + 3 k  lambda a[1]/ d  + \
2  2  2                2  2                 2  2
-8 alpha  k  v  a[2] + 16 alpha  k  v a[2] - 8 alpha  k  a[2]

2  2           2             2     \
+ 2 k  v  a[2] - 4 k  v a[2] + 2 k  a[2]/ d

2  2                         3          4
+ 4 alpha  k  lambda v a[2] + 2 L a[0]  - 4 alpha  a[0]

2                         2  2
- 48 L alpha  a[0] a[1] a[2] + 4 alpha  k  lambda mu a[1]

2  2                2
- 4 alpha  k  lambda a[2] - k  lambda v a[2]

2                                         2
- k  lambda mu a[1] + 12 L a[0] a[1] a[2] + k  lambda a[2]

2     3                              2
- 8 L alpha  a[0]  - 12 a[0] a[1] a[2] - 4 alpha  beta a[0]

2                          3         /          2     3
+ alpha  a[0] + beta a[0] - 2 a[0]  = 0, 15 \-8 L alpha  a[1]

3         3\  4
+ 2 L a[1]  - 2 a[1] / d

/           2          2                2              2\
+ 10 \-24 L alpha  a[0] a[1]  + 6 L a[0] a[1]  - 6 a[0] a[1] /

3     /           2     2                  2     2
d  + 6 \-24 L alpha  a[0]  a[1] - 24 L alpha  a[1]  a[2]

4                2                2
- 4 alpha  a[1] + 6 L a[0]  a[1] + 6 L a[1]  a[2]

2                  2              2
- 4 alpha  beta a[1] + alpha  a[1] - 6 a[0]  a[1]

2                 \  2   /        2  2
- 6 a[1]  a[2] + beta a[1]/ d  + \12 alpha  k  lambda v a[1]

2  2                  2
- 12 alpha  k  lambda a[1] - 3 k  lambda v a[1]

2            \  3     /       2  2
+ 3 k  lambda a[1]/ d  + 3 \4 alpha  k  lambda mu a[1]

2     3             2
- 8 L alpha  a[0]  - 48 L alpha  a[0] a[1] a[2]

4         2                          3
- 4 alpha  a[0] - k  lambda mu a[1] + 2 L a[0]

2                  2
+ 12 L a[0] a[1] a[2] - 4 alpha  beta a[0] + alpha  a[0]

3                                \       /       2  2
- 2 a[0]  - 12 a[0] a[1] a[2] + beta a[0]/ d + 3 \4 alpha  k

2               2  2                    2  2
lambda  a[1] + 8 alpha  k  mu v a[1] - 8 alpha  k  mu a[1]

2       2           2                2        \  2   /
- k  lambda  a[1] - 2 k  mu v a[1] + 2 k  mu a[1]/ d  + \
2  2                         2  2
-12 alpha  k  lambda v a[2] + 12 alpha  k  lambda a[2]

2                    2            \
+ 3 k  lambda v a[2] - 3 k  lambda a[2]/ d

2  2                   2                   2
+ 8 alpha  k  mu v a[2] - 6 a[0]  a[2] - 6 a[1] a[2]

4               2  2       2
- 4 alpha  a[2] + 4 alpha  k  lambda  a[2]

2  2              2
- 8 alpha  k  mu a[2] - 2 k  mu v a[2]

2     2                  2          2
- 24 L alpha  a[0]  a[2] - 24 L alpha  a[1] a[2]

2       2           2                   2
- k  lambda  a[2] + 2 k  mu a[2] + 6 L a[0]  a[2]

2          2                  2
+ 6 L a[1] a[2]  - 4 alpha  beta a[2] + alpha  a[2]

2  2  2                 2     3
+ beta a[2] = 0, 8 alpha  k  v  a[1] - 8 L alpha  a[1]

2  2                 2  2           2  2
- 16 alpha  k  v a[1] + 8 alpha  k  a[1] - 2 k  v  a[1]

3      2             2              3    \
+ 2 L a[1]  + 4 k  v a[1] - 2 k  a[1] - 2 a[1]  = 0 },
/

\
{alpha, a[0], a[1], a[2]}|
/

## how to get multi kink solution from func...

Maple

restart;
A[0] := 0;
0
A[1] := sqrt(2*(k[1]^2-w[1]^2))/n;
(1/2)
/      2         2\
\2 k[1]  - 2 w[1] /
------------------------
n
A[2] := sqrt(2*(k[2]^2-w[2]^2))/n;
(1/2)
/      2         2\
\2 k[2]  - 2 w[2] /
------------------------
n
c[1] := 1;
1
c[2] := 1;
1
c[3] := 1;
1
c[4] := 1;
1
c[5] := 1;
1
c[6] := 1;
1
k[1] := 10.5;
10.5
k[2] := 3.5;
3.5
w[1] := 5.05;
5.05
w[2] := .5;
0.5
m := 1.9;
1.9
n := 1.75;
1.75
xi[1] := -t*w[1]+x*k[1];
-5.05 t + 10.5 x
xi[2] := -t*w[2]+x*k[2];
-0.5 t + 3.5 x
a := m/sqrt(2*(k[1]^2-w[1]^2));
0.1459402733
b := m/sqrt(k[2]^2-w[2]^2);
0.5484827558
g := a*(c[2]*exp(a*xi[1])+c[3]*exp(-a*xi[1]));
0.1459402733 exp(-0.7369983802 t + 1.532372870 x)

+ 0.1459402733 exp(0.7369983802 t - 1.532372870 x)
h := c[1]+c[2]*exp(a*xi[1])+c[3]*exp(-a*xi[1]);
1 + exp(-0.7369983802 t + 1.532372870 x)

+ exp(0.7369983802 t - 1.532372870 x)
G := b*(c[5]*exp(b*xi[2])+c[6]*exp(-b*xi[2]));
0.5484827558 exp(-0.2742413779 t + 1.919689645 x)

+ 0.5484827558 exp(0.2742413779 t - 1.919689645 x)
H := c[4]+c[5]*exp(b*xi[2])+c[6]*exp(-b*xi[2]);
1 + exp(-0.2742413779 t + 1.919689645 x)

+ exp(0.2742413779 t - 1.919689645 x)
u := A[0]+A[1]*[g/h]+A[2]*[G/H];
[(2.799416849 (0.5484827558 exp(-0.2742413779 t + 1.919689645 x)

+ 0.5484827558 exp(0.2742413779 t - 1.919689645 x)))/(1

+ exp(-0.2742413779 t + 1.919689645 x)

+ exp(0.2742413779 t - 1.919689645 x)) + (7.439442594

(0.1459402733 exp(-0.7369983802 t + 1.532372870 x)

+ 0.1459402733 exp(0.7369983802 t - 1.532372870 x)))/(1

+ exp(-0.7369983802 t + 1.532372870 x)

+ exp(0.7369983802 t - 1.532372870 x))]
plot3d(u, x = -20 .. .20, t = -20 .. .20);

t := 0;
0
plot(u, x = -15 .. 15);

Error, (in plot) found points with fewer or more than 2 components

## help for get some good figure...

Maple 18

fgure set 1;
Error, missing operation
Typesetting:-mambiguous(fgure Typesetting:-mambiguous(set 1,

Typesetting:-merror("missing operation")))
restart;
l := 4;
4
m := 1;
1
n := 2;
2
k := 1/sqrt(-6*beta*l^2+24*beta*m*n);
1
----------------
(1/2)
4 (-3 beta)
w := alpha/(5*beta*sqrt(l^2-4*m*n));
(1/2)
alpha 2
------------
20 beta

B[0] := -(1/25)*alpha*(5*l^3/(5*sqrt(l^2-4*m*n))-20*l*m*n/(5*sqrt(l^2-4*m*n))-l^2+2*m*n)*sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n))/((l^2-4*m*n)^2*beta);
/   (1/2)     \          (1/2)  (1/2)
alpha \8 2      - 12/ (-3 beta)      2
- -------------------------------------------
40 beta
B[1] := -(12/5)*m*alpha*(5*l/(5*sqrt(l^2-4*m*n))-1)/sqrt(-6*beta*l^2+24*beta*m*n);
/ (1/2)    \
3 alpha \2      - 1/
- --------------------
(1/2)
5 (-3 beta)
B[2] := -12*m^2*alpha/(sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n)));
(1/2)
3 alpha 2
- -----------------
(1/2)
20 (-3 beta)
theta := sqrt(l^2-4*m*n);
(1/2)
2 2
xi[0] := 1;
1
F := -l/(2*m)-theta*tanh((1/2)*theta*(xi+xi[0]))/(2*m);
(1/2)     / (1/2)         \
-2 - 2      tanh\2      (xi + 1)/
beta := -2;
-2
alpha := -3;
-3

1

xi := k*x-t*w;
1   (1/2)     3     (1/2)
-- 6      x - -- t 2
24            40
u := B[0]+B[1]*F+B[2]*F*F;
3  /   (1/2)     \  (1/2)  (1/2)   3  / (1/2)    \  (1/2) /
- -- \8 2      - 12/ 6      2      + -- \2      - 1/ 6      |-2
80                                 10                     \

(1/2)     / (1/2) /1   (1/2)     3     (1/2)    \\\   3
- 2      tanh|2      |-- 6      x - -- t 2      + 1||| + --
\       \24            40             ///   40

(1/2)  (1/2)
6      2

2
/      (1/2)     / (1/2) /1   (1/2)     3     (1/2)    \\\
|-2 - 2      tanh|2      |-- 6      x - -- t 2      + 1|||
\                \       \24            40             ///
plot3d(u, x = -30 .. .30, t = -30 .. .30);

t := 0;
0
plot([u], x = -30 .. 30);

case2222;
case2222
restart;
l := 2;
2
m := 1;
1
n := 2;
2
k := 1/sqrt(-6*beta*l^2+24*beta*m*n);
(1/2)
6
------------
(1/2)
12 beta
w := alpha/(5*beta*sqrt(l^2-4*m*n));
1
-- I alpha
10
- ----------
beta

B[0] := -(1/25)*alpha*(5*l^3/(5*sqrt(l^2-4*m*n))-20*l*m*n/(5*sqrt(l^2-4*m*n))-l^2+2*m*n)*sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n))/((l^2-4*m*n)^2*beta);
(1/2)
alpha 6
------------
(1/2)
5 beta
B[1] := -(12/5)*m*alpha*(5*l/(5*sqrt(l^2-4*m*n))-1)/sqrt(-6*beta*l^2+24*beta*m*n);
/1   1  \        (1/2)
|- + - I| alpha 6
\5   5  /
----------------------
(1/2)
beta
B[2] := -12*m^2*alpha/(sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n)));
1           (1/2)
-- I alpha 6
10
-----------------
(1/2)
beta
theta := sqrt(l^2-4*m*n);
2 I
xi[0] := 1;
1
C := -2;
-2
F := -l/(2*m)-theta*tanh((1/2)*theta*xi)/(2*m)+sech((1/2)*theta*xi)/(C*cosh((1/2)*theta*xi)-2*m*sinh((1/2)*theta*xi)/theta);
sec(xi)
-1 + tan(xi) + --------------------
-2 cos(xi) - sin(xi)

beta := -2;
-2
alpha := 3;
3

xi := k*x-t*w;
1   (1/2)     (1/2)     3
- -- 6      (-2)      x - -- I t
24                      20
u := B[0]+B[1]*F+B[2]*F*F;
3   (1/2)     (1/2)   /  3    3   \  (1/2)     (1/2) /
- -- 6      (-2)      + |- -- - -- I| 6      (-2)      |-1
10                    \  10   10  /                  \

/1   (1/2)     (1/2)     3     \   /   /1   (1/2)
- tan|-- 6      (-2)      x + -- I t| + |sec|-- 6
\24                      20    /   \   \24

(1/2)     3     \\//      /1   (1/2)     (1/2)     3     \
(-2)      x + -- I t|| |-2 cos|-- 6      (-2)      x + -- I t|
20    // \      \24                      20    /

/1   (1/2)     (1/2)     3     \\\   3     (1/2)
+ sin|-- 6      (-2)      x + -- I t||| - -- I 6
\24                      20    ///   20

(1/2) /        /1   (1/2)     (1/2)     3     \   /   /1
(-2)      |-1 - tan|-- 6      (-2)      x + -- I t| + |sec|--
\        \24                      20    /   \   \24

(1/2)     (1/2)     3     \\//
6      (-2)      x + -- I t|| |
20    // \
/1   (1/2)     (1/2)     3     \
-2 cos|-- 6      (-2)      x + -- I t|
\24                      20    /

/1   (1/2)     (1/2)     3     \\\
+ sin|-- 6      (-2)      x + -- I t|||^2
\24                      20    ///
plot3d(Re(u), x = -30 .. .30, t = -30 .. .30);

t := 0;
0
plot([Re(u)], x = -30 .. 30);

plot3d(Im(u), x = -10 .. .10, t = -10 .. .10);
Error, (in plot3d) bad range arguments: x = -10 .. .10, 0 = -10 .. .10
t := 0;
0
plot([Im(u)], x = -30 .. 30);

fgure set 2;
Error, missing operation
Typesetting:-mambiguous(fgure Typesetting:-mambiguous(set 2,

Typesetting:-merror("missing operation")))
restart;
l := 4;
4
m := 1;
1
n := 2;
2
k := 1/sqrt(6*beta*l^2-24*beta*m*n);
(1/2)
3
------------
(1/2)
12 beta
w := alpha/((5*sqrt(l^2-4*m*n))*beta);
(1/2)
alpha 2
------------
20 beta

B[0] := (1/25)*alpha*(5*l^3/(5*sqrt(l^2-4*m*n))-20*l*m*n/(5*sqrt(l^2-4*m*n))+l^2-6*m*n)*sqrt(6*beta*l^2-24*beta*m*n)*(5*sqrt(l^2-4*m*n))/((l^2-4*m*n)^2*beta);
/   (1/2)    \  (1/2)  (1/2)
alpha \8 2      + 4/ 3      2
----------------------------------
(1/2)
40 beta
B[1] := -(12/5)*m*alpha*(5*l/(5*sqrt(l^2-4*m*n))-1)/sqrt(6*beta*l^2-24*beta*m*n);
/ (1/2)    \  (1/2)
alpha \2      - 1/ 3
- -------------------------
(1/2)
5 beta
B[2] := -12*m^2*alpha/(sqrt(6*beta*l^2-24*beta*m*n)*(5*sqrt(l^2-4*m*n)));
(1/2)  (1/2)
alpha 3      2
- -------------------
(1/2)
20 beta

1           (1/2)
-- I alpha 6
10
-----------------
(1/2)
beta
theta := sqrt(l^2-4*m*n);
(1/2)
2 2
xi[0] := 1;
1
F := -l/(2*m)-theta*tanh((1/2)*theta*(xi+xi[0]))/(2*m);
(1/2)     / (1/2)         \
-2 - 2      tanh\2      (xi + 1)/
beta := -2;
-2
alpha := -3;
-3

1

xi := k*x-t*w;
1   (1/2)     (1/2)     3     (1/2)
- -- 3      (-2)      x - -- t 2
24                      40
u := B[0]+B[1]*F+B[2]*F*F;
3  /   (1/2)    \     (1/2)  (1/2)  (1/2)   3  / (1/2)    \
-- \8 2      + 4/ (-2)      3      2      - -- \2      - 1/
80                                          10

(1/2)     (1/2) /
3      (-2)      |-2
\

(1/2)     / (1/2) /  1   (1/2)     (1/2)     3     (1/2)
- 2      tanh|2      |- -- 3      (-2)      x - -- t 2
\       \  24                      40

\\\   3   (1/2)     (1/2)  (1/2) /
+ 1||| - -- 3      (-2)      2      |-2
///   40                         \

(1/2)     / (1/2) /  1   (1/2)     (1/2)     3     (1/2)
- 2      tanh|2      |- -- 3      (-2)      x - -- t 2
\       \  24                      40

\\\
+ 1|||^2
///
plot3d(Re(u), x = -30 .. .30, t = -30 .. .30);
Error, (in plot3d) bad range arguments: x = -30 .. .30, 0 = -30 .. .30
t := 0;
0
plot([Re(u)], x = -30 .. 30);

plot3d(Im(u), x = -1 .. 1, t = -1 .. 1);
Error, (in plot3d) bad range arguments: x = -1 .. 1, 0 = -1 .. 1
t := 0;
0
plot([Im(u)], x = -30 .. 30);

case2222;
case2222
restart;
l := 2;
2
m := 1;
1
n := 2;
2
k := 1/sqrt(-6*beta*l^2+24*beta*m*n);
(1/2)
6
------------
(1/2)
12 beta
w := alpha/(5*beta*sqrt(l^2-4*m*n));
1
-- I alpha
10
- ----------
beta

B[0] := -(1/25)*alpha*(5*l^3/(5*sqrt(l^2-4*m*n))-20*l*m*n/(5*sqrt(l^2-4*m*n))-l^2+2*m*n)*sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n))/((l^2-4*m*n)^2*beta);
(1/2)
alpha 6
------------
(1/2)
5 beta
B[1] := -(12/5)*m*alpha*(5*l/(5*sqrt(l^2-4*m*n))-1)/sqrt(-6*beta*l^2+24*beta*m*n);
/1   1  \        (1/2)
|- + - I| alpha 6
\5   5  /
----------------------
(1/2)
beta
B[2] := -12*m^2*alpha/(sqrt(-6*beta*l^2+24*beta*m*n)*(5*sqrt(l^2-4*m*n)));
1           (1/2)
-- I alpha 6
10
-----------------
(1/2)
beta
theta := sqrt(l^2-4*m*n);
2 I
xi[0] := 1;
1
C := -2;
-2
F := -l/(2*m)-theta*tanh((1/2)*theta*xi)/(2*m)+sech((1/2)*theta*xi)/(C*cosh((1/2)*theta*xi)-2*m*sinh((1/2)*theta*xi)/theta);
sec(xi)
-1 + tan(xi) + --------------------
-2 cos(xi) - sin(xi)

beta := -2;
-2
alpha := 3;
3

xi := k*x-t*w;
1   (1/2)     (1/2)     3
- -- 6      (-2)      x - -- I t
24                      20
u := B[0]+B[1]*F+B[2]*F*F;
3   (1/2)     (1/2)   /  3    3   \  (1/2)     (1/2) /
- -- 6      (-2)      + |- -- - -- I| 6      (-2)      |-1
10                    \  10   10  /                  \

/1   (1/2)     (1/2)     3     \   /   /1   (1/2)
- tan|-- 6      (-2)      x + -- I t| + |sec|-- 6
\24                      20    /   \   \24

(1/2)     3     \\//      /1   (1/2)     (1/2)     3     \
(-2)      x + -- I t|| |-2 cos|-- 6      (-2)      x + -- I t|
20    // \      \24                      20    /

/1   (1/2)     (1/2)     3     \\\   3     (1/2)
+ sin|-- 6      (-2)      x + -- I t||| - -- I 6
\24                      20    ///   20

(1/2) /        /1   (1/2)     (1/2)     3     \   /   /1
(-2)      |-1 - tan|-- 6      (-2)      x + -- I t| + |sec|--
\        \24                      20    /   \   \24

(1/2)     (1/2)     3     \\//
6      (-2)      x + -- I t|| |
20    // \
/1   (1/2)     (1/2)     3     \
-2 cos|-- 6      (-2)      x + -- I t|
\24                      20    /

/1   (1/2)     (1/2)     3     \\\
+ sin|-- 6      (-2)      x + -- I t|||^2
\24                      20    ///
plot3d(Re(u), x = -30 .. .30, t = -30 .. .30);

t := 0;
0
plot([Re(u)], x = -30 .. 30);

plot3d(Im(u), x = -10 .. .10, t = -10 .. .10);
Error, (in plot3d) bad range arguments: x = -10 .. .10, 0 = -10 .. .10
t := 0;
0
plot([Im(u)], x = -30 .. 30);

## solve figure draw problem...

Maple 18

Figure;
Figure
restart;
A[0] := 0;
0
A[1] := sqrt(2*(k[1]^2-w[1]^2))/sqrt(lambda);
(1/2)
/      2         2\
\2 k[1]  - 2 w[1] /
------------------------
(1/2)
lambda
A[2] := sqrt(2*(k[2]^2-w[2]^2))/sqrt(lambda);
(1/2)
/      2         2\
\2 k[2]  - 2 w[2] /
------------------------
(1/2)
lambda
c[1] := 1;
1
c[2] := 1;
1
c[3] := 1;
1
c[4] := 1;
1
c[5] := 1;
1
c[6] := 1;
1
k[1] := 10.5;
10.5
k[2] := 3.5;
3.5
w[1] := 5.05;
5.05
w[2] := .5;
0.5
m := 1.9;
1.9
lambda := 1.75;
1.75
xi[1] := -t*w[1]+x*k[1];
-5.05 t + 10.5 x
xi[2] := -t*w[2]+x*k[2];
-0.5 t + 3.5 x
a := m/sqrt(k[1]^2-w[1]^2);
0.2063907138
b := m/sqrt(k[2]^2-w[2]^2);
0.5484827558
g := a*(c[2]*cos(a*xi[1])-c[3]*sin(a*xi[1]));
0.2063907138 cos(2.167102495 x) - 0.2063907138 sin(2.167102495 x)
h := c[1]+c[2]*sin(a*xi[1])+c[3]*cos(a*xi[1]);
1 + sin(2.167102495 x) + cos(2.167102495 x)
G := b*(c[5]*cos(b*xi[2])-c[6]*sin(b*xi[2]));
0.5484827558 cos(1.919689645 x) - 0.5484827558 sin(1.919689645 x)
H := c[4]+c[5]*sin(b*xi[2])+c[6]*cos(b*xi[2]);
1 + sin(1.919689645 x) + cos(1.919689645 x)
u := A[0]+A[1]*[g/h]+A[2]*[G/H];
[                     1
[------------------------------------------- (3.703280398
[1 + sin(1.919689645 x) + cos(1.919689645 x)

(0.5484827558 cos(1.919689645 x)

- 0.5484827558 sin(1.919689645 x))) +

1
------------------------------------------- (9.841457496
1 + sin(2.167102495 x) + cos(2.167102495 x)

(0.2063907138 cos(2.167102495 x)

]
- 0.2063907138 sin(2.167102495 x)))]
]
plot3d(Re(u), x = -20 .. .20, t = -20 .. .20);
Error, invalid input: `simpl/Re` expects its 1st argument, x, to be of type {boolean, algebraic}, but received [3.703280398*(.5484827558*cos(1.919689645*x)-.5484827558*sin(1.919689645*x))/(1+sin(1.919689645*x)+cos(1.919689645*x))+9.841457496*(.2063907138*cos(2.167102495*x)-.2063907138*sin(2.167102495*x))/(1+sin(2.167102495*x)+cos(2.167102495*x))]
t := 0;
0
plot(u, x = -15 .. 15);

## Fix error missing operation...

Maple 18

restart;
solve({12 beta k^2 w alpha[2]+k alpha[2]^2, 56 beta k^2 m w alpha[2]+4 beta k^2 w alpha[1]-4 A k^2 alpha[2]+8 k m alpha[2]^2+2 k alpha[1] alpha[2]0, 104 beta k^2 m^2 w alpha[2]+16 K beta k^2 w alpha[2]+16 beta k^2 m w alpha[1]-20 A k^2 m alpha[2]+28 k m^2 alpha[2]^2-2 A k^2 alpha[1]+14 k m alpha[1] alpha[2]+2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2], 56 k alpha[2]^2 m^3+42 k alpha[1] alpha[2] m^2+6 m (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+96 w k^2 beta alpha[2] m^3+40 w k^2 beta alpha[2] K m-40 A k^2 alpha[2] m^2-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]+4 w k^2 beta alpha[1] K+4 (8 K beta k^2 w alpha[2]-2 A k^2 alpha[1]) m+24 w k^2 beta alpha[1] m^2,70 k alpha[2]^2 m^4+70 k alpha[1] m^3 alpha[2]+15 m^2 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+5 (-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m+80 w k^2 beta alpha[2] K m^2-40 A k^2 alpha[2] m^3+44 w k^2 beta alpha[2] m^4+4 w k^2 beta alpha[2] K^2-2 A k^2 alpha[1] K+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]+16 w k^2 beta alpha[1] K m+6 (8 K beta k^2 w alpha[2]-2 A k^2 alpha[1]) m^2+16 w k^2 beta alpha[1] m^3-4 w k^2 beta beta[1] m+2 A k^2 beta[1]+4 w k^2 beta beta[2],56 k alpha[2]^2 m^5+70 k alpha[1] alpha[2] m^4+20 m^3 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+10 (-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m^2+80 w k^2 beta alpha[2] K m^3-20 A k^2 alpha[2] m^4+8 w k^2 beta alpha[2] m^5+4 (4 K^2 beta k^2 w alpha[2]-2 A K k^2 alpha[1]+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]) m+24 w k^2 beta alpha[1] K m^2+4 (8 K beta k^2 w alpha[2]-2 A k^2 alpha[1]) m^3+4 w k^2 beta alpha[1] m^4+2 k alpha[0] beta[1]+2 k alpha[1] beta[2]-2 w beta[1]-4 w k^2 beta beta[1] m^2+4 w k^2 beta beta[1] K+4 A k^2 beta[1] m-8 w k^2 beta beta[2] m+4 A k^2 beta[2],28 k alpha[2]^2 m^6+42 k alpha[1] alpha[2] m^5+15 m^4 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+10 (-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m^3+40 w k^2 beta alpha[2] K m^4-4 A k^2 alpha[2] m^5+6 (4 K^2 beta k^2 w alpha[2]-2 A K k^2 alpha[1]+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]) m^2+16 w k^2 beta alpha[1] K m^3+(8 K beta k^2 w alpha[2]-2 A k^2 alpha[1]) m^4+3 (2 k alpha[0] beta[1]+2 k alpha[1] beta[2]-2 w beta[1]) m-8 w k^2 beta beta[1] K m+2 A k^2 beta[1] m^2+2 A k^2 beta[1] K+2 k alpha[0] beta[2]+k beta[1]^2-2 w beta[2]+16 w k^2 beta beta[2] K+(8 K beta k^2 w beta[1]+4 A k^2 beta[2]) m,8 k alpha[2]^2 m^7+14 k alpha[1] alpha[2] m^6+6 m^5 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+5 (-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m^4+8 w k^2 beta alpha[2] K m^5+4 (4 K^2 beta k^2 w alpha[2]-2 A K k^2 alpha[1]+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]) m^3+4 w k^2 beta alpha[1] K m^4+3 (2 k alpha[0] beta[1]+2 k alpha[1] beta[2]-2 w beta[1]) m^2+2 (2 A K k^2 beta[1]+2 k alpha[0] beta[2]+k beta[1]^2-2 w beta[2]) m-4 w k^2 beta beta[1] K m^2+4 w k^2 beta beta[1] K^2-8 w k^2 beta beta[2] K m+4 A k^2 beta[2] K+2 k beta[1] beta[2],k m^8 alpha[2]^2+2 k m^7 alpha[1] alpha[2]+m^6 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+(-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m^5+(4 K^2 beta k^2 w alpha[2]-2 A K k^2 alpha[1]+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]) m^4+(2 k alpha[0] beta[1]+2 k alpha[1] beta[2]-2 w beta[1]) m^3+(2 A K k^2 beta[1]+2 k alpha[0] beta[2]+k beta[1]^2-2 w beta[2]) m^2+(4 K^2 beta k^2 w beta[1]+4 A K k^2 beta[2]+2 k beta[1] beta[2]) m+12 w k^2 beta beta[2] K^2+k beta[2]^2},{k,w, alpha[0], alpha[1], beta[1], alpha[2], beta[2]});
Error, missing operation

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