Integrable multi-component generalization of a modified short pulse equation

TL;DR

This paper introduces a multi-component generalization of the modified short pulse equation, demonstrating its integrability through Lax pairs, conservation laws, and soliton solutions, including cusp solitons and breathers, with detailed interaction analysis.

Contribution

It presents a new integrable multi-component system extending the modified short pulse equation, with explicit soliton solutions and analysis of their interactions and properties.

Findings

The system admits Lax pairs and infinite conservation laws.

Cusp solitons and breathers are shown to exist under certain conditions.

Interaction of cusp solitons results in calculable phase shifts.

Abstract

We propose a multi-component generalization of the modified short pulse (SP) equation which was derived recently as a reduction of Feng's two-component SP equation. Above all, we address the two-component system in depth. We obtain the Lax pair, an infinite nember of conservation laws and multisoliton solutions for the system, demonstrating its integrability. Subsequently, we show that the two-component system exhibits cusp solitons and breathers for which the detailed analysis is performed. Specifically, we explore the interaction process of two cusp solitons and derive the formula for the phase shift. While cusp solitons are singular solutions, smooth breather solutions are shown to exist, provided that the parameters characterizing the solutions satisfy certain condition. Last, we discuss the relation between the proposed system and existing two-component SP equations.