Numerical inverse scattering for the sine-Gordon equation

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 et al. (2012). 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. (C) 2019 Elsevier B.V. All rights reserved.