I am stuck on nonlinear one dimensional coupled,anyone has any idea how to solve the following equation on maple to reach exact solution.help is highly appriciated.

pde[1] := diff(u(x, t), t)-1constant*(diff(u(x, t), x, x)) = alpha*u(x, t)*(1-v(x, t))

pde[2] := diff(v(x, t), t)-2constant*(diff(v(x, t), x, x)) = beta*v(x, t)*(1-u(x, t))

Thank you for help.

I see these methods follow theta scheme which i could not understand.let me work more if i feel something not understadable, will ask you more regarding nonlinear f-kpp equation 

Thank you.

I am sorry D and E are just constants.In my previous post,that equation is coupled Fisher-KPP equation.I am trying to get Exact Solution.As I do not get from any research paper.So i am trying to get Exact solution.

Once agai thank you