Numerical Solitons of Generalized Korteweg-de Vries Equations

TL;DR

This paper introduces a numerical approach to find solitary wave solutions of generalized Korteweg-de Vries equations, including soliton interactions, on unbounded domains with artificial boundary conditions.

Contribution

It presents a novel numerical method for solving nonlinear eigenvalue problems for GKdV equations, addressing unbounded domains and complex soliton interactions.

Findings

Successfully computed soliton solutions for K(m,n) and KdV-K(m,n) equations.

Observed collision behaviors of solitons and antisolitons.

Demonstrated effectiveness of artificial boundary conditions in numerical simulations.

Abstract

We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We specially discuss the soliton solutions of the K(m, n) equation and KdV-K(m,n) equation. Furthermore for the mixed models of linear and nonlinear dispersion, the collision behaviors of soliton-soliton and soliton-antisoliton are observed.