KdV equation beyond standard assumptions on initial data

2017/10/09 by Alexei Rybkin · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf · doi:10.1016/j.physd.2017.10.005

To appear in Physica D: nonlinear phenomena

arxiv created 2017/10/09 · arxiv updated 2018/01/17

Abstract

We show that the Cauchy problem for the KdV equation can be solved by the inverse scattering transform (IST) for any initial data bounded from below, decaying sufficiently rapidly at plus infinity, but unrestricted otherwise. Thus our approach doesn't require any boundary condition at minus infinity.

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• Self-similar asymptotics in the decay problem for the Volterra lattice with zero boundary condition

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