Numerical inverse scattering for the sine-Gordon equation

2018/06/27 by Bernard Deconinck, Thomas Trogdon, Xin Yang · 1 citation
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1016/j.physd.2019.05.007

arxiv created 2018/06/27 · arxiv updated 2019/09/04

Abstract

We implement the numerical inverse scattering transform (NIST) for the sine-Gordon equation in laboratory coordinates on the real line using the method developed by Trogdon, Olver and Deconinck. The NIST allows one to compute the solution at any x and t without having spatial discretization or time-stepping. The numerical implementation is fully spectrally accurate. With the help of the method of nonlinear steepest descent, the NIST is demonstrated to be uniformly accurate.

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• Numerical inverse scattering transform for the coupled modified Korteweg-de Vries equation

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