equ:=2*(-wu2*w12*JacobiDN(w12*tanh(t*wt1 + wx1*x + b5)^2, m)*JacobiSN(w12*tanh(t*wt1 + wx1*x + b5)^2, m) + wu3*w13 + wu4*w14)*wt1*tanh(t*wt1 + wx1*x + b5)*sech(t*wt1 + wx1*x + b5)^2 + 2*(-wu2*w12*JacobiDN(w12*tanh(t*wt1 + wx1*x + b5)^2, m)*JacobiSN(w12*tanh(t*wt1 + wx1*x + b5)^2, m) + wu3*w13 + wu4*w14)*wx1*tanh(t*wt1 + wx1*x + b5)*sech(t*wt1 + wx1*x + b5)^2 + 2*omega*(b5 + wu2*JacobiCN(w12*tanh(t*wt1 + wx1*x + b5)^2, m) + wu3*w13*tanh(t*wt1 + wx1*x + b5)^2 + wu4*w14*tanh(t*wt1 + wx1*x + b5)^2)*(-wu2*w12*JacobiDN(w12*tanh(t*wt1 + wx1*x + b5)^2, m)*JacobiSN(w12*tanh(t*wt1 + wx1*x + b5)^2, m) + wu3*w13 + wu4*w14)*wx1*tanh(t*wt1 + wx1*x + b5)*sech(t*wt1 + wx1*x + b5)^2 - (48*tanh(t*wt1 + wx1*x + b5)*wx1*sech(t*wt1 + wx1*x + b5)^8*(sinh(t*wt1 + wx1*x + b5)^2*JacobiSN(w12*tanh(t*wt1 + wx1*x + b5)^2, m)^3*JacobiDN(w12*tanh(t*wt1 + wx1*x + b5)^2, m)*m^2*w12^3*wu2 + JacobiCN(w12*tanh(t*wt1 + wx1*x + b5)^2, m)*cosh(t*wt1 + wx1*x + b5)^2*m^2*w12^2*wu2*(cosh(t*wt1 + wx1*x + b5)^2 - 3/2)*JacobiSN(w12*tanh(t*wt1 + wx1*x + b5)^2, m)^2 - (2*JacobiSN(w12*tanh(t*wt1 + wx1*x + b5)^2, m)*(-cosh(t*wt1 + wx1*x + b5)^6/4 + (3*cosh(t*wt1 + wx1*x + b5)^4)/4 + sinh(t*wt1 + wx1*x + b5)^2*w12^2*(m^2 + 1/4))*w12*wu2*JacobiDN(w12*tanh(t*wt1 + wx1*x + b5)^2, m))/3 - cosh(t*wt1 + wx1*x + b5)^2*(3*(cosh(t*wt1 + wx1*x + b5)^2 - 3/2)*w12^2*wu2*JacobiCN(w12*tanh(t*wt1 + wx1*x + b5)^2, m) + cosh(t*wt1 + wx1*x + b5)^2*(cosh(t*wt1 + wx1*x + b5)^2 - 3)*(w13*wu3 + w14*wu4))/6)*wt1^2)*NULL

restart;

T := R(xi)*R(xi) + lambda;

u := A[0] + A[1]*R(xi) + B[1]/R(xi);

d[1] := A[1]*T - B[1]*T/R(xi)^2;

d[2] := 2*A[1]*R(xi)*T - 2*B[1]*T/R(xi) + 2*B[1]*(R(xi)^2 + lambda)*T/R(xi)^3;

expand(((-alpha^2*b^2 + a^2)*alpha^2)/(2*beta)*d[2] + (omega + alpha^2*(alpha^2*l^2 + k^2)/2 - a*C[1]/(-alpha^2*b^2 + a^2))*u[0]/(beta - 2*beta*a^2/(-alpha^2*b^2 + a^2)) + u[0]*u[0]*u[0]);

value(%);

simplify(%);

collect(%, R(xi));

      /      6  4    4      2\      3
 A[1] \-alpha  b  + a  alpha / R(xi) 
 ------------------------------------
             /     2  2    2\        
        beta \alpha  b  + a /        

                  /      6  4    4      2\         
      A[1] lambda \-alpha  b  + a  alpha / R(xi)   
    + ------------------------------------------ + 
                     /     2  2    2\              
                beta \alpha  b  + a /              

                         /                               /     
             1           |/                    B[1] \    |     
   --------------------- ||A[0] + A[1] R(xi) + -----|[0] |beta 
        /     2  2    2\ \\                    R(xi)/    \     
   beta \alpha  b  + a /                                       

                                                  2
   /     2  2    2\ /                    B[1] \    
   \alpha  b  + a / |A[0] + A[1] R(xi) + -----|[0] 
                    \                    R(xi)/    

      1  2  2      6   1 /  2  2    2  2\      4
    + - b  l  alpha  + - \-a  l  + b  k / alpha 
      2                2                        

                                                       \\
      /  1  2  2    2      \      2    2               ||
    + |- - a  k  + b  omega| alpha  - a  omega + a C[1]||
      \  2                 /                           //

                  /      6  4    4      2\
      B[1] lambda \-alpha  b  + a  alpha /
    + ------------------------------------
               /     2  2    2\           
          beta \alpha  b  + a / R(xi)     

            6  4       2         4      2       2     
      -alpha  b  lambda  B[1] + a  alpha  lambda  B[1]
    + ------------------------------------------------
                     /     2  2    2\      3          
                beta \alpha  b  + a / R(xi)           

restart;
with(plottools);
with(plots);
a := 1;
b := 1;
c := 1;
k := 1;
l := 1;
omega := 1;
A[2] = 2;
alpha := 2;
beta := 1;
kappa := 0.5;
C[1] := 1;
lambda := -1;

omega := (-alpha^6*b^4*lambda + 2*alpha^6*b^2*l^2 - 2*a^2*alpha^4*l^2 + 2*alpha^4*b^2*k^2 + a^4*alpha^2*lambda - 2*a^2*alpha^2*k^2 + 4*a*C[1])/(-4*alpha^2*b^2 + 4*a^2);

a[0] := 0;

a[1] := sqrt(-(-alpha^2*b^2 + a^2)/(4*beta))*alpha;

b[1] := sqrt(-(alpha^2*b^2*lambda*sigma - a^2*lambda*sigma)/(4*beta))*alpha;

sigma := A[1]*A[1] - A[2]*A[2];

T := A[1]*sinh(xi*sqrt(-lambda)) + A[2]*cosh(xi*sqrt(-lambda)) + mu/lambda;

t := diff(T, xi);

S := t/T;

R := 1/T;

mu := 0;

A[1] := 0;

y := 0;

xi := k*x^kappa/kappa + l*y^kappa/kappa - omega*t^kappa/kappa;

  Error, recursive assignment

restart;
solve({-alpha^4*b^2*lambda*mu*b[1] + a^2*alpha^2*lambda*mu*b[1] + 6*beta*lambda^2*sigma*a[0]*a[1]^2 + 6*beta*mu^2*a[0]*a[1]^2 - 6*beta*lambda*a[0]*b[1]^2 = 0, -alpha^4*b^2*lambda^2*mu*sigma - alpha^4*b^2*mu^3 + a^2*alpha^2*lambda^2*mu*sigma + a^2*alpha^2*mu^3 - 4*beta*lambda^2*sigma*a[0]*b[1] - 4*beta*lambda*mu*b[1]^2 - 4*beta*mu^2*a[0]*b[1] = 0, -alpha^4*b^2*lambda^2*sigma - alpha^4*b^2*mu^2 + a^2*alpha^2*lambda^2*sigma + a^2*alpha^2*mu^2 + beta*lambda^2*sigma*a[1]^2 + beta*mu^2*a[1]^2 - 3*beta*lambda*b[1]^2 = 0, -alpha^4*b^2*lambda^2*sigma - alpha^4*b^2*mu^2 + a^2*alpha^2*lambda^2*sigma + a^2*alpha^2*mu^2 + 3*beta*lambda^2*sigma*a[1]^2 + 3*beta*mu^2*a[1]^2 - beta*lambda*b[1]^2 = 0, -alpha^6*b^4*lambda^2*mu*b[1] + alpha^6*b^2*l^2*lambda^2*sigma*a[0] + alpha^6*b^2*l^2*mu^2*a[0] - a^2*alpha^4*l^2*lambda^2*sigma*a[0] + alpha^4*b^2*k^2*lambda^2*sigma*a[0] - a^2*alpha^4*l^2*mu^2*a[0] + alpha^4*b^2*k^2*mu^2*a[0] + 2*alpha^2*b^2*beta*lambda^2*sigma*a[0]^3 + a^4*alpha^2*lambda^2*mu*b[1] - a^2*alpha^2*k^2*lambda^2*sigma*a[0] - 6*alpha^2*b^2*beta*lambda^2*a[0]*b[1]^2 + 2*alpha^2*b^2*beta*mu^2*a[0]^3 - a^2*alpha^2*k^2*mu^2*a[0] + 2*a^2*beta*lambda^2*sigma*a[0]^3 + 2*alpha^2*b^2*lambda^2*omega*sigma*a[0] - 6*a^2*beta*lambda^2*a[0]*b[1]^2 + 2*a^2*beta*mu^2*a[0]^3 + 2*alpha^2*b^2*mu^2*omega*a[0] - 2*a^2*lambda^2*omega*sigma*a[0] - 2*a^2*mu^2*omega*a[0] + 2*a*lambda^2*sigma*C[1]*a[0] + 2*a*mu^2*C[1]*a[0] = 0, -2*alpha^6*b^4*lambda^3*sigma - 2*alpha^6*b^4*lambda*mu^2 + alpha^6*b^2*l^2*lambda^2*sigma + alpha^6*b^2*l^2*mu^2 - a^2*alpha^4*l^2*lambda^2*sigma + alpha^4*b^2*k^2*lambda^2*sigma + 2*a^4*alpha^2*lambda^3*sigma - a^2*alpha^4*l^2*mu^2 + alpha^4*b^2*k^2*mu^2 + 6*alpha^2*b^2*beta*lambda^2*sigma*a[0]^2 + 2*a^4*alpha^2*lambda*mu^2 - a^2*alpha^2*k^2*lambda^2*sigma - 6*alpha^2*b^2*beta*lambda^2*b[1]^2 + 6*alpha^2*b^2*beta*mu^2*a[0]^2 - a^2*alpha^2*k^2*mu^2 + 6*a^2*beta*lambda^2*sigma*a[0]^2 + 2*alpha^2*b^2*lambda^2*omega*sigma - 6*a^2*beta*lambda^2*b[1]^2 + 6*a^2*beta*mu^2*a[0]^2 + 2*alpha^2*b^2*mu^2*omega - 2*a^2*lambda^2*omega*sigma - 2*a^2*mu^2*omega + 2*a*lambda^2*sigma*C[1] + 2*a*mu^2*C[1] = 0, -alpha^6*b^4*lambda^3*sigma + alpha^6*b^4*lambda*mu^2 + alpha^6*b^2*l^2*lambda^2*sigma + alpha^6*b^2*l^2*mu^2 - a^2*alpha^4*l^2*lambda^2*sigma + alpha^4*b^2*k^2*lambda^2*sigma + a^4*alpha^2*lambda^3*sigma - a^2*alpha^4*l^2*mu^2 + alpha^4*b^2*k^2*mu^2 + 6*alpha^2*b^2*beta*lambda^2*sigma*a[0]^2 - a^4*alpha^2*lambda*mu^2 - a^2*alpha^2*k^2*lambda^2*sigma - 2*alpha^2*b^2*beta*lambda^2*b[1]^2 + 12*alpha^2*b^2*beta*lambda*mu*a[0]*b[1] + 6*alpha^2*b^2*beta*mu^2*a[0]^2 - a^2*alpha^2*k^2*mu^2 + 6*a^2*beta*lambda^2*sigma*a[0]^2 + 2*alpha^2*b^2*lambda^2*omega*sigma - 2*a^2*beta*lambda^2*b[1]^2 + 12*a^2*beta*lambda*mu*a[0]*b[1] + 6*a^2*beta*mu^2*a[0]^2 + 2*alpha^2*b^2*mu^2*omega - 2*a^2*lambda^2*omega*sigma - 2*a^2*mu^2*omega + 2*a*lambda^2*sigma*C[1] + 2*a*mu^2*C[1] = 0}, {omega, a[0], a[1], b[1]});
 

restart;
alias(u = u(x, y, t), f = f(x, y, t));
                              u, f
u := (f+sqrt(R))*exp(I*R*t);
                    /     (1/2)\           
                    \f + R     / exp(I R t)
pde1 := I*(diff(u, t))+diff(u, x, x)+2*lambda*u*abs(u)*abs(u)-gamma*(diff(u, x, t));
   // d   \                /     (1/2)\             \
 I ||--- f| exp(I R t) + I \f + R     / R exp(I R t)|
   \\ dt  /                                         /

      / d  / d   \\           
    + |--- |--- f|| exp(I R t)
      \ dx \ dx  //           

               /     (1/2)\                           2 
    + 2 lambda \f + R     / exp(I R t) (exp(-Im(R t)))  

               2
   |     (1/2)| 
   |f + R     | 

            // d  / d   \\                / d   \             \
    - gamma ||--- |--- f|| exp(I R t) + I |--- f| R exp(I R t)|
            \\ dx \ dt  //                \ dx  /             /