A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
Mathematical Physics
2015-06-16 v2 math.MP
Numerical Analysis
Abstract
In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x,t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t.
Keywords
Cite
@article{arxiv.1305.5616,
title = {A numerical dressing method for the nonlinear superposition of solutions of the KdV equation},
author = {Thomas Trogdon and Bernard Deconinck},
journal= {arXiv preprint arXiv:1305.5616},
year = {2015}
}