I'm sorry for the bad texting,
I want to solve this partial differential equation but i can't due to wrong encoding i think. If is solvable can someone write me the right code?
this is the equation:
D[D[f[x,t],x],x] + D[D[f[x,y],y],y] - (1/x)*D[f[x,y],x] +(x^2)f[x,y] + f[x,y]^3 - af[x,y]=0
f[x,0]=1 f[0,y]=1 f'[x,0]=0 f'[0,y]=0
do i need more boundary conditions??
It looks like a non-linear Poisson Eqn modified by an advection term in the $x$ dimension and I think you meant to use a $y$ and not a $t$ in the first term. If so, then your equation is
$$ \frac{\partial^2f}{\partial x^2} +\frac{\partial^2f}{\partial y^2} - \frac{1}{x}\frac{\partial f}{\partial x} + x^2f+f^3-af=0 $$
where $f=f(x,y)$
You have all the boundary conditions that you need. I doubt (you could check Carslaw and Jaeger to be sure) that there is a closed form solution and the best approach would be to use finite differences with under-relaxation. Also, look up the Peaceman-Rachford ADI agorithm.
I would pay special attention to the advection term which becomes unbounded at $x=0$