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Numerical Inverse Scattering for the KdV Equation Revisited

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

We consider the numerical evaluation of the forward and inverse scattering transforms for the Korteweg-de Vries (KdV) equation. For the initial-value problem (IVP) for decaying data on the line, we review existing numerical techniques and discuss successes using new basis functions. Extensions of these ideas to step-like data and to the IVP with periodic initial data will also be discussed. The latter requires a recent approach to the numerical computation of the so-called Baker-Akhiezer function of a large-genus hyperelliptic Riemann surface. All approaches produce accurate numerical solutions in the long-time regime.

This talk is part of the Isaac Newton Institute Seminar Series series.

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