Integrable multi-component generalization of a modified short pulse equation

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.

Ver. 2, Typos corrected, A related paper: Y. Matsuno, J. Math. Phys. 52, 123702 (2011)

References in corpus (10)

• The short pulse equation is integrable
• Solitary wave solutions of the short pulse equation
• Ultra-short pulses in linear and nonlinear media
• The Bi-Hamiltonian Structure of the Short Pulse Equation
• Complex short pulse and coupled complex short pulse equations
• A novel multi-component generalization of the short pulse equation and its multisoliton solutions
• On integrability of the vector short pulse equation
• Transformation and integrability of a generalized short pulse equation
• Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
• Soliton and Periodic solutions of the Short Pulse Model Equation

Cited by in corpus (4)

• Lax Representations for Matrix Short Pulse Equations
• Integrability of a generalized short pulse equation revisited
• Parametric solutions of the generalized short pulse equations
• Discontinuous Galerkin methods for short pulse type equations via hodograph transformations