Breather and interacting soliton and periodic waves for modified KdV equation

TL;DR

This paper discovers exact localized and periodic wave solutions, including breathers and interacting solitons, for the modified KdV equation, highlighting the influence of nonlinearity sign on their existence and potential applications.

Contribution

It introduces a new class of exact solutions for the modified KdV equation, emphasizing the role of nonlinearity sign in their existence and properties.

Findings

Existence of breather and interacting soliton solutions depends on nonlinearity sign.

Solutions include both localized and periodic waves with joint parameters.

Wave structures exhibit properties with potential practical applications.

Abstract

We present the discovery of a class of exact spatially localized as well as periodic wave solutions within the framework of the modified Korteweg-de Vries equation. This class comprises breather and interacting soliton solutions as well as interacting periodic wave solutions. The functional forms of these solutions include a joint parameter which can take both positive and negative values of unity. It is found that the existence of those closed form solutions depend strongly on whether the cubic nonlinearity parameter should be considered positive or negative. The derived wave structures show interesting properties that may find practical applications.