## 55 Reputation

8 years, 226 days

## fix error and identify any other wrong a...

Maple

> {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
>

## Why error in plot3d?...

Maple

> 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);

 5 6 7 Page 7 of 7
﻿