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arXiv · 1806.10709

Numerical inverse scattering for the sine-Gordon equation

Bernard Deconinck·Thomas Trogdon·Xin Yang
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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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Bernard Deconinck, Thomas Trogdon, Xin Yang. 2018-06-27. Numerical inverse scattering for the sine-Gordon equation. https://doi.org/10.1016/j.physd.2019.05.007

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