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Numerical inverse scattering for the Korteweg–-de Vries and modified Korteweg–-de Vries equations

Abstract:

Recent advances in the numerical solution of Riemann–Hilbert problems allow for the implementation of a Cauchy initial value problem solver for the Korteweg–de Vries equation (KdV) and the defocusing modified Korteweg–de Vries equation (mKdV), without any boundary approximation. Borrowing ideas from the method of nonlinear steepest descent, this method is demonstrated to be asymptotically accurate. The method is straightforward for the case of defocusing mKdV due to the lack of poles in the R...

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Thomas Trogdon More by this author
Sheehan Olver More by this author
Bernard Deconinck More by this author
Publication date:
2011-08-05
URN:
uuid:caf44d12-63dd-43f2-86f5-840eada78528
Local pid:
oai:eprints.maths.ox.ac.uk:1397

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