# Question:set up equations and find parameter

## Question:set up equations and find parameter

Maple
restart;
with(PolynomialTools);
with(RootFinding);
with(SolveTools);
with(LinearAlgebra);
NULL;
NULL;
E1 := (-alpha*k^2*A[1] - alpha*k^2*B[1] + 3*A[0]^2*A[1]*beta[4] + 3*A[0]^2*B[1]*beta[4] + A[1]^3*beta[4] + 3*A[1]^2*B[1]*beta[4] + 3*A[1]*B[1]^2*beta[4] + B[1]^3*beta[4] + 2*A[0]*A[1]*beta[3] + 2*A[0]*B[1]*beta[3] - w*A[1] - w*B[1])*cosh(xi)^6 + (-alpha*k^2*A[0] + A[0]^3*beta[4] + 3*A[0]*A[1]^2*beta[4] + 6*A[0]*A[1]*B[1]*beta[4] + 3*A[0]*B[1]^2*beta[4] + A[0]^2*beta[3] + A[1]^2*beta[3] + 2*A[1]*B[1]*beta[3] + B[1]^2*beta[3] - w*A[0])*sinh(xi)*cosh(xi)^5 + (2*alpha*k^2*A[1] + alpha*k^2*B[1] - 2*alpha*lambda^2*A[1] + 2*alpha*lambda^2*B[1] - 2*gamma*lambda^2*A[1] + 2*gamma*lambda^2*B[1] - 6*A[0]^2*A[1]*beta[4] - 3*A[0]^2*B[1]*beta[4] - 3*A[1]^3*beta[4] - 6*A[1]^2*B[1]*beta[4] - 3*A[1]*B[1]^2*beta[4] - 4*A[0]*A[1]*beta[3] - 2*A[0]*B[1]*beta[3] + 2*w*A[1] + w*B[1])*cosh(xi)^4 + (alpha*k^2*A[0] - A[0]^3*beta[4] - 6*A[0]*A[1]^2*beta[4] - 6*A[0]*A[1]*B[1]*beta[4] - A[0]^2*beta[3] - 2*A[1]^2*beta[3] - 2*A[1]*B[1]*beta[3] + w*A[0])*sinh(xi)*cosh(xi)^3 + (-alpha*k^2*A[1] + 4*alpha*lambda^2*A[1] + 4*gamma*lambda^2*A[1] + 3*A[0]^2*A[1]*beta[4] + 3*A[1]^3*beta[4] + 3*A[1]^2*B[1]*beta[4] + 2*A[0]*A[1]*beta[3] - w*A[1])*cosh(xi)^2 + (3*A[0]*A[1]^2*beta[4] + A[1]^2*beta[3])*sinh(xi)*cosh(xi) - 2*alpha*lambda^2*A[1] - 2*gamma*lambda^2*A[1] - A[1]^3*beta[4] = 0;
N := 6;
for i from 0 to N do
equ[1][i] := coeff(E1, {cosh(xi)^i, sinh(xi)^i}, i) = 0;
end do;
//        2               2
equ[1][0] := \\-alpha k  A[1] - alpha k  B[1]

2                      2                    3
+ 3 A[0]  A[1] beta[4] + 3 A[0]  B[1] beta[4] + A[1]  beta[4]

2                           2               3
+ 3 A[1]  B[1] beta[4] + 3 A[1] B[1]  beta[4] + B[1]  beta[4]

\
+ 2 A[0] A[1] beta[3] + 2 A[0] B[1] beta[3] - w A[1] - w B[1]/

6   /        2            3
cosh(xi)  + \-alpha k  A[0] + A[0]  beta[4]

2
+ 3 A[0] A[1]  beta[4] + 6 A[0] A[1] B[1] beta[4]

2               2               2
+ 3 A[0] B[1]  beta[4] + A[0]  beta[3] + A[1]  beta[3]

2                 \
+ 2 A[1] B[1] beta[3] + B[1]  beta[3] - w A[0]/ sinh(xi)

5   /         2               2
cosh(xi)  + \2 alpha k  A[1] + alpha k  B[1]

2                      2
- 2 alpha lambda  A[1] + 2 alpha lambda  B[1]

2                      2
- 2 gamma lambda  A[1] + 2 gamma lambda  B[1]

2                      2
- 6 A[0]  A[1] beta[4] - 3 A[0]  B[1] beta[4]

3                 2
- 3 A[1]  beta[4] - 6 A[1]  B[1] beta[4]

2
- 3 A[1] B[1]  beta[4] - 4 A[0] A[1] beta[3]

\         4   /
- 2 A[0] B[1] beta[3] + 2 w A[1] + w B[1]/ cosh(xi)  + \alpha

2            3                      2
k  A[0] - A[0]  beta[4] - 6 A[0] A[1]  beta[4]

2                 2
- 6 A[0] A[1] B[1] beta[4] - A[0]  beta[3] - 2 A[1]  beta[3]

\                  3   /
- 2 A[1] B[1] beta[3] + w A[0]/ sinh(xi) cosh(xi)  + \
2                      2                      2
-alpha k  A[1] + 4 alpha lambda  A[1] + 4 gamma lambda  A[1]

2                      3
+ 3 A[0]  A[1] beta[4] + 3 A[1]  beta[4]

2                                            \
+ 3 A[1]  B[1] beta[4] + 2 A[0] A[1] beta[3] - w A[1]/

2
cosh(xi)

/           2               2        \
+ \3 A[0] A[1]  beta[4] + A[1]  beta[3]/ sinh(xi) cosh(xi)

2                      2            3
- 2 alpha lambda  A[1] - 2 gamma lambda  A[1] - A[1]  beta[4] =

\
0/ = 0

equ[1][1] := 0 = 0

equ[1][2] := 0 = 0

equ[1][3] := 0 = 0

equ[1][4] := 0 = 0

equ[1][5] := 0 = 0

equ[1][6] := 0 = 0

NULL;
NULL;