Soliton solutions in the class of implicit difference schemes

TL;DR

This paper investigates the emergence of soliton solutions in a class of implicit difference schemes derived from Euler's method, revealing unusual behaviors and discussing applications to nonlinear problems.

Contribution

It introduces a detailed numerical analysis of implicit difference schemes showing soliton phenomena, a novel observation in this context.

Findings

Soliton solutions arise in certain implicit difference schemes.

Unusual behaviors are observed in the numerical schemes.

Applications to nonlinear problems are discussed.

Abstract

We announce a detailed numerical investigation for some class of difference schemes, which arises from Euler implicit scheme. Such schemes demonstrate unusual behavior and leads to origin of solitons. Applications to some nonlinear problems are discussed.