Construction of soliton solutions of the matrix modified Korteweg-de Vries equation

TL;DR

This paper develops an explicit formula for solutions of the matrix modified KdV equation, extending previous results and exploring new solutions with diverse qualitative properties.

Contribution

The authors present a comprehensive solution formula for the matrix mKdV equation, including new solutions beyond previously studied subclasses.

Findings

Constructed solutions beyond known subclasses.

Analyzed qualitative properties of new solutions.

Extended the solution framework for the matrix mKdV equation.

Abstract

An explicit solution formula for the matrix modified KdV equation is presented, which comprises the solutions given in Ref. 7 (S. Carillo, M. Lo Schiavo, and C. Schiebold. Matrix solitons solutions of the modified Korteweg-de Vries equation. In: Nonlinear Dynamics of Structures, Systems and Devices, edited by W. Lacarbonara, B. Balachandran, J. Ma, J. Tenreiro Machado, G. Stepan (Springer, Cham, 2020), pp. 75-83). In fact, the solutions in Ref.7 are part of a subclass studied in detail by the authors in a forthcoming publication. Here several solutions beyond this subclass are constructed and discussed with respect to qualitative properties.