Basic concept Q ,non-linear PDE , kdv

[binbagsss]

U_t+6UU_x+U_xxx=0 [kdv eq]

Why to solve this do you need U(x,t=0)?
Why is it a initial value problem?

This should probably be really obvious. I think I've forgotten some basic background stuff, just starting my course in solitons...

Thanks for your help.​

 

[binbagsss]

Sorry I'm not sure how , if you can, edit your threads on the new layout..

Some thoughts:
- If we have U(x,t=0) and solve for U(x,t) , is our solution only valid for t in a small interval around t=0? Or can we solve for all t from this?

 

[binbagsss]

bump.

 

[HallsofIvy]

Your question doesn't make sense. You don't "have to have" a value for U(x, 0). While that, together with values for U(a, t) and U(a, b), would be sufficient since the partial differential equation is of first order in t and second order in x, it is NOT necessary.