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Question: How to resolve an equation with pdsolve? KDV equation, Problem with IBC

Question:How to resolve an equation with pdsolve? KDV equation, Problem with IBC

manT 10
pdsolve condition
March 28 2014
2

Hi ,

I would like to resolve the Kortweg and de Devries equation :

> KDV2:= diff( u(X,T), T)+ 6*u(X,T)*diff(u(X,T),X)+ diff(u(X,T),X$3);

 

I used pdsolve but I have a problem to enter the IBC :

I want

u(infinity, t) =0
u( -infinity, t )=0

u ( x, 0 ) = 1


So I did :


> SOL:=pdsolve(diff( u(X,T), T)+ 6*u(X,T)*diff(u(X,T),X)+ diff(u(X,T),X$3)=0,{u(-10, T) = 0, u(10, T) = 0, u(X, 0) =1},numeric,time=T,range=-10..10);

 

But it doesn't work.

( I remplace infinity by 10 because then I want the graphic representation of the solution )

Could you help me please ?  
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