Integrable multi-component generalization of a modified short pulse equation

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 number 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 conditions. Last, we discuss the relation between the proposed system and existing two-component SP equations.

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