Numerical inverse scattering for the sine-Gordon equation
Exactly Solvable and Integrable Systems
2019-09-04 v1
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.
Cite
@article{arxiv.1806.10709,
title = {Numerical inverse scattering for the sine-Gordon equation},
author = {Bernard Deconinck and Thomas Trogdon and Xin Yang},
journal= {arXiv preprint arXiv:1806.10709},
year = {2019}
}