bashar27

fix simplify problem...

Asked: bashar27 55 Product: Maple 18

May 22 2019

1 1

restart;
lambda := 1;
1
mu := 1;
1
alpha := 1;
1
v := 2;
2
delta := 1;
1
m := 1;
1
d := 3;
3
l := 1;
1
omega := -(1/2)*a*lambda^2-a*m^2+2*a*mu*v-delta*l*m-(1/2)*delta*lambda^2+2*delta*mu*v-l^2*mu-(1/2)*lambda^2*mu+2*mu^2*v-2*a*mu-2*delta*mu-2*mu^2;
1
- a + 1
2
a[0] := ((2*d*v-2*d-lambda)*(1/2))*sqrt(2)*sqrt(gamma*(a+delta+mu))/gamma;
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma
a[1] := 0;
0
a[2] := -(2*(1/2))*sqrt(2)*sqrt(gamma*(a+delta+mu))*(d^2*v-d^2-d*lambda+mu)/gamma;
(1/2) (1/2)
7 2 (gamma (a + 2))
- -----------------------------
gamma
Omega := lambda^2-4*mu*v+4*mu;
-3
H := (-lambda+sqrt(-Omega)*tan((1/2)*sqrt(-Omega)*xi))/(2*(v-1));
1 1 (1/2) /1 (1/2) \
- - + - 3 tan|- 3 xi|
2 2 \2 /
u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2)
7 2 (gamma (a + 2))
- -------------------------------------
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //

eta := -l*y-m*x+omega*t;
/1 \
-y - x + |- a + 1| t
\2 /
u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2)
7 2 (gamma (a + 2))
- -------------------------------------
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //

f := diff(u, xi);
/ 2\
(1/2) (1/2) |3 3 /1 (1/2) \ |
7 2 (gamma (a + 2)) |- + - tan|- 3 xi| |
\4 4 \2 / /
-------------------------------------------------------
2
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //
S := diff(u, xi);
/ 2\
(1/2) (1/2) |3 3 /1 (1/2) \ |
7 2 (gamma (a + 2)) |- + - tan|- 3 xi| |
\4 4 \2 / /
-------------------------------------------------------
2
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //
xi := x+y-(-2*alpha*m-delta*l-delta*m-2*l*mu)*t;
x + y + 6 t
eq := (-omega-a*m*m-delta*l*m-mu*l*l)*u-(gamma*u*u)*u+(a+delta+mu)*S;
/ (1/2) (1/2)
/ 3 \ |5 2 (gamma (a + 2))
|- - a - 3| |-----------------------------
\ 2 / | 2 gamma
|
\

(1/2) (1/2) \ /
7 2 (gamma (a + 2)) | |
- ------------------------------------------------| - gamma |
/5 1 (1/2) /1 (1/2) \\| |
gamma |- + - 3 tan|- 3 (x + y + 6 t)||| |
\2 2 \2 /// \

(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|^3 +
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///

/
1 |
------------------------------------------------- |7 (a + 2)
2 \
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 (x + y + 6 t)||
\2 2 \2 //

/ 2
(1/2) (1/2) |3 3 /1 (1/2) \
2 (gamma (a + 2)) |- + - tan|- 3 (x + y + 6 t)|
\4 4 \2 /

\\
||
||
//
value(%);
/ (1/2) (1/2)
/ 3 \ |5 2 (gamma (a + 2))
|- - a - 3| |-----------------------------
\ 2 / | 2 gamma
|
\

(1/2) (1/2) \ /
7 2 (gamma (a + 2)) | |
- ------------------------------------------------| - gamma |
/5 1 (1/2) /1 (1/2) \\| |
gamma |- + - 3 tan|- 3 (x + y + 6 t)||| |
\2 2 \2 /// \

(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|^3 +
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///

/
1 |
------------------------------------------------- |7 (a + 2)
2 \
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 (x + y + 6 t)||
\2 2 \2 //

/ 2
(1/2) (1/2) |3 3 /1 (1/2) \
2 (gamma (a + 2)) |- + - tan|- 3 (x + y + 6 t)|
\4 4 \2 /

\\
||
||
//

simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion

fix the problem pls...

Asked: bashar27 55 Product: Maple 18

May 22 2019

1 0

Q := exp(I*(-y-x+((1/2)*a+1)*t))*((5/2)*sqrt(2)*sqrt(gamma*(a+2))/gamma-7*sqrt(2)*sqrt(gamma*(a+2))/(gamma*(5/2+(1/2)*sqrt(3)*tan((1/2)*sqrt(3)*(x+y+6*t)))));
/ (1/2) (1/2)
/ / /1 \ \\ |5 2 (gamma (a + 2))
exp|I |-y - x + |- a + 1| t|| |-----------------------------
\ \ \2 / // | 2 gamma
|
\

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///
/ (1/2) (1/2)
/ / /1 \ \\ |5 2 (gamma (a + 2))
exp|I |-y - x + |- a + 1| t|| |-----------------------------
\ \ \2 / // | 2 gamma
|
\

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///
plot3d(Re(Q), x = -40 .. -37, y = -40 .. -37, t = -10 .. 10);

fix the solve problem pls...

Asked: bashar27 55 Product: Maple 18

May 21 2019

1 0

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...

Asked: bashar27 55 Product: Maple

February 13 2019

1 1

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...

Asked: bashar27 55 Product: Maple 18

February 13 2019

1 0

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);

E-Mail Address:
Password:
Remember Me:	Automatically sign in on future visits

E-Mail Address:
Password:
Remember Me:	Automatically sign in on future visits

Ask a Question

Create a Post

55 Reputation

5 Badges

MaplePrimes Activity

These are questions asked by bashar27

fix simplify problem...

fix the problem pls...

fix the solve problem pls...

how to get multi kink solution from func...

help for get some good figure...

Save this setting as your default sorting preference?

Ask a Question

Create a Post

Generating PDF…

Save this setting as your default sorting preference?
Note: You can change your preference any time in your account settings
Don't show this again

From:
To:

Custom Message (optional):