# Question:checking the solution

## Question:checking the solution

Maple

I have a complex PDE as follows:

where u(x, t) is a complex function.

The following function u_11(x, t) is a solution for the PDE above.

where

I want to check whether the u_11(x,t) is a solution for the PDE or NOT.

How to correctly define the complex PDE in MAPLE?

```PDE:=I*diff(u(x,t),t)+diff(u(x,t),x\$2)+alpha*(abs(u(x,t))^2)*u(x,t)+ I*( gamma[1]*diff(u(x,t),x\$3) + gamma[2]*(abs(u(x,t))^2)*u(x,t) + gamma[3]*diff((abs(u(x,t))^2),x)*u(x,t) )=0;

```

or

```PDE:=I*diff(u(x,t),t)+diff(u(x,t),x\$2)+alpha*(evalc(abs(u(x,t))^2))*u(x,t)+ I*( gamma[1]*diff(u(x,t),x\$3) + gamma[2]*(evalc(abs(u(x,t))^2))*u(x,t) + gamma[3]*diff((evalc(abs(u(x,t))^2)),x)*u(x,t) )=0;
```

Let's check the solution is right or not:

```k:=(gamma[2]+2*gamma[3]-3*gamma[1]*alpha)/(6*gamma[1]*gamma[3]);
omega:=(((1-3*gamma[1]*k)*(2*k-c-3*gamma[1]*(k^2))  )/(gamma[1]))+(k^2)-gamma[1]*(k^3);

uu[11]:=1/(gamma[2]+2*gamma[3])^(1/2)*(-3*(3*k^2*gamma[1]+c-2*k))^(1/2 )*sin(1/2/gamma[1]*2^(1/2)*(gamma[1]*(3*k^2*gamma[1]+c-2*k))^(1/2)*(-c*t+x))/ cos(1/2/gamma[1]*2^(1/2)*(gamma[1]*(3*k^2*gamma[1]+c-2*k))^(1/2)*(-c*t+x))*exp( I*(k*x-omega*t));
```
`pdetest(u(x,t)=uu[11],PDE);`

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