对跃迁耦合非线性薛定谔方程的平面波/周期背景上的怪波与呼吸波的相互作用解

Abstract

Abstract:

In this paper, we explore the pair-transition-coupled nonlinear Schrödinger equations, which can describe the propagation of orthogonally polarized optical waves. According to the Lax pair, the $N$-fold generalized Darboux transformation can be constructed. As applications, choosing distinct seed solutions, we obtain interactions of diverse types of novel rogue waves and breathers on the plane wave/periodic background. Especially, it is observed that some of rogue waves and breathers with special wave shapes are extremely different from other common rogue waves and breathers. Moreover, the position, angle, structure and energy distribution of these solutions influenced by parameters are exhibited graphically and we discuss their interaction properties. These results will shed light on the study of localized waves on the various backgrounds for other integrable systems.

Key words: pair-transition-coupled nonlinear Schrödinger equations, generalized Darboux transformation, rogue waves, breathers, periodic background

CLC Number:

O175.24

Gaojie Lu, Wenyun Zhang, Yi Zhang, Yu Lou. Interactions of Rogue Waves and Breathers On the Plane Wave/Periodic Background for the Pair-Transition-Coupled Nonlinear Schrödinger Equations[J].Acta mathematica scientia,Series A, 2026, 46(5): 1742-1750.

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References 29

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Interactions of Rogue Waves and Breathers On the Plane Wave/Periodic Background for the Pair-Transition-Coupled Nonlinear Schrödinger Equations

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