bashar27

25 Reputation

4 Badges

4 years, 55 days

MaplePrimes Activity


These are questions asked by bashar27

> restart;
> u := c-6*mu*(1+lambda*sqrt(-mu)*coth(A+sqrt(-mu)*(x+y+mu*t)))/((a+b)*sqrt(-mu)*coth(A+sqrt(-mu)*(x+y+mu*t)))+6*mu*sqrt(sigma*(1-coth(A+sqrt(-mu)*(x+y+mu*t))^2))/(sqrt(sigma)*(a+b)*sqrt(-mu)*coth(A+sqrt(-mu)*(x+y+mu*t)));
            /                (1/2)     /         (1/2)               \\
       6 mu \1 + lambda (-mu)      coth\A + (-mu)      (x + y + mu t)//
   c - ----------------------------------------------------------------
                         (1/2)     /         (1/2)               \     
            (a + b) (-mu)      coth\A + (-mu)      (x + y + mu t)/     

                                                                 (1/2)   
               /      /                                       2\\        
               |      |        /         (1/2)               \ ||        
          6 mu \sigma \1 - coth\A + (-mu)      (x + y + mu t)/ //        
      + -----------------------------------------------------------------
             (1/2)              (1/2)     /         (1/2)               \
        sigma      (a + b) (-mu)      coth\A + (-mu)      (x + y + mu t)/
> c := 1;
                                      1
> mu := -1.5;
                                     1.5
> lambda := 1.5;
                                     1.5
> a := 1;
                                      1
> b := 1;
                                      1
> A := .5;
                                     0.5
> y := 0;
                                      0
> plot3d([abs(u)], x = -10 .. 3, t = -10 .. 3);
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

 

> restart;
> u := a[0]-12*sqrt(mu)*(1+lambda*sqrt(mu)*tan(A-sqrt(mu)*(x+y+4*mu*t)))/((a+b)*tan(A-sqrt(mu)*(x+y+4*mu*t)));
              (1/2) /             (1/2)    /      (1/2)                 \\
         12 mu      \1 + lambda mu      tan\A - mu      (x + y + 4 mu t)//
  a[0] - -----------------------------------------------------------------
                                /      (1/2)                 \            
                     (a + b) tan\A - mu      (x + y + 4 mu t)/            
> a[0] := 2;
                                      2
> mu := 1.5;
                                     1.5
> lambda := 2;
                                      2
> a := .5;
                                     0.5
> b := .5;
                                     0.5
> A := 1.5;
                                     1.5
> y := 0;
                                      0
> plot3d([abs(u)], x = -3 .. 3, t = -3 .. 3);
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

> {w = -4*mu, a[-1] = -12*mu/(a+b), a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0, b[1] = 0};
  /                     12 mu                                              
 { w = -4 mu, a[-1] = - -----, a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0,
  \                     a + b                                              

           \
   b[1] = 0 }
           /
> restart;
>
> w := -4*mu;
                                    -4 mu
> a[-1] := -12*mu/(a+b);
                                     12 mu
                                   - -----
                                     a + b
> a[0] := a[0];
                                    a[0]
> a[1] := 0;
                                      0
> b[-1] := 0;
                                      0
> b[0] := 0;
                                      0
> b[1] := 0;
                                      0
> xi := x+w*t;
                                 x - 4 mu t
> P := sqrt(mu)*tan(A-sqrt(mu)*xi);
                      (1/2)    /      (1/2)             \
                    mu      tan\A - mu      (x - 4 mu t)/
> u := a[0]+a[1]*P/(1+lambda*P)+a[-1]*(1+lambda*P)/P+b[0]*sqrt(sigma*(1+P^2/mu))/P+b[1]*sqrt(sigma*(1+P^2/mu))+b[-1]*sqrt(sigma*(1+P^2/mu))/P^2;
                (1/2) /             (1/2)    /      (1/2)             \\
           12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
    a[0] - -------------------------------------------------------------
                                  /      (1/2)             \            
                       (a + b) tan\A - mu      (x - 4 mu t)/            
> Diff(u, x, t)+a*(Diff(u, x))*(Diff(u, x, y))+b*(Diff(u, `$`(x, 2)))*(Diff(u, y))+Diff(u, `$`(x, 3), y);
/   2   /            (1/2) /             (1/2)    /      (1/2)             \\\
|  d    |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|
|------ |a[0] - -------------------------------------------------------------|
| dt dx |                              /      (1/2)             \            |
\       \                   (a + b) tan\A - mu      (x - 4 mu t)/            /

  \     /    /    
  |     | d  |    
  | + a |--- |a[0]
  |     | dx |    
  /     \    \    

          (1/2) /             (1/2)    /      (1/2)             \\\\ /   2   /
     12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |  d    |
   - -------------------------------------------------------------|| |------ |
                            /      (1/2)             \            || | dy dx |
                 (a + b) tan\A - mu      (x - 4 mu t)/            // \       \

              (1/2) /             (1/2)    /      (1/2)             \\\\     /
         12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||     |
  a[0] - -------------------------------------------------------------|| + b |
                                /      (1/2)             \            ||     |
                     (a + b) tan\A - mu      (x - 4 mu t)/            //     \

   2 /            (1/2) /             (1/2)    /      (1/2)             \\\\ /
  d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |
  -- |a[0] - -------------------------------------------------------------|| |
     |                              /      (1/2)             \            || |
     \                   (a + b) tan\A - mu      (x - 4 mu t)/            // \

      /            (1/2) /             (1/2)    /      (1/2)             \\\\
   d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||
  --- |a[0] - -------------------------------------------------------------||
   dy |                              /      (1/2)             \            ||
      \                   (a + b) tan\A - mu      (x - 4 mu t)/            //

     / 4 /            (1/2) /             (1/2)    /      (1/2)             \\
     |d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
   + |-- |a[0] - -------------------------------------------------------------
     |   |                              /      (1/2)             \            
     \   \                   (a + b) tan\A - mu      (x - 4 mu t)/            

  \\
  ||
  ||
  ||
  //
> value(%);
                       /                                 2\
              3        |       /      (1/2)             \ |
         96 mu  lambda \1 + tan\A - mu      (x - 4 mu t)/ /
         --------------------------------------------------
                               a + b                       

                                                                2   
                            /                                 2\    
                   3        |       /      (1/2)             \ |    
              96 mu  lambda \1 + tan\A - mu      (x - 4 mu t)/ /    
            - --------------------------------------------------- +
                                                         2          
                               /      (1/2)             \           
                    (a + b) tan\A - mu      (x - 4 mu t)/           

                                                  /             
                                                  |             
                             1                    |     (5/2) /
           -------------------------------------- \96 mu      \1
                                                3               
                      /      (1/2)             \                
           (a + b) tan\A - mu      (x - 4 mu t)/                

                       (1/2)    /      (1/2)             \\
            + lambda mu      tan\A - mu      (x - 4 mu t)//

                                               2\   
           /                                 2\ |   
           |       /      (1/2)             \ | |   
           \1 + tan\A - mu      (x - 4 mu t)/ / / -

                                                 /             
                             1                   |     (5/2) /
           ------------------------------------- \96 mu      \1
                      /      (1/2)             \               
           (a + b) tan\A - mu      (x - 4 mu t)/               

                                                            /
                       (1/2)    /      (1/2)             \\ |
            + lambda mu      tan\A - mu      (x - 4 mu t)// \1

                                           2\\
                 /      (1/2)             \ ||
            + tan\A - mu      (x - 4 mu t)/ //
> simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion
>

 

> restart;
> u := -3*sqrt(mu)*tanh*(A+sqrt(-mu)*(x-(1/2)*mu*t))/sqrt(6*a)+3*sqrt(mu)*sech*(A+sqrt(-mu)*(x-(1/2)*mu*t))/sqrt(-6*a);

>
> mu := .5;
0.5
> lambda := 1;
1
> a := 0.5e-1;
0.05
> A := 1.5;
1.5
> plot3d([abs(u)], x = -3 .. 3, t = -3 .. 3);

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