English

Spectral approach to Korteweg-de Vries equations on the compactified real line

Numerical Analysis 2021-12-21 v1 Numerical Analysis Exactly Solvable and Integrable Systems

Abstract

We present a numerical approach for generalised Korteweg-de Vries (KdV) equations on the real line. In the spatial dimension we compactify the real line and apply a Chebyshev collocation method. The time integration is performed with an implicit Runge-Kutta method of fourth order. Several examples are discussed: initial data bounded but not vanishing at infinity as well as data not satisfying the Faddeev condition, i.e. with a slow decay towards infinity.

Keywords

Cite

@article{arxiv.2112.09952,
  title  = {Spectral approach to Korteweg-de Vries equations on the compactified real line},
  author = {C. Klein and N. Stoilov},
  journal= {arXiv preprint arXiv:2112.09952},
  year   = {2021}
}