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);
