Basic concept Q ,non-linear PDE , kdv

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Homework Help Overview

The discussion revolves around the Korteweg-de Vries (KdV) equation, a non-linear partial differential equation (PDE). The original poster questions the necessity of an initial condition, U(x, t=0), and seeks clarification on the nature of initial value problems in the context of this equation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of having an initial condition for the solution of the KdV equation, questioning whether the solution is valid only in a limited time interval or for all time. There is also a challenge to the necessity of the initial condition itself.

Discussion Status

The discussion is ongoing, with participants expressing differing views on the necessity of the initial condition for the KdV equation. Some guidance has been offered regarding the sufficiency of certain conditions, but no consensus has been reached.

Contextual Notes

The original poster indicates a lack of familiarity with foundational concepts related to solitons and initial value problems, suggesting a potential gap in background knowledge that may influence the discussion.

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Ut+6UUx+Uxxx=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.​
 
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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?
 
bump.
 
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.
 

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