推广的导数非线性薛定谔方程的单/双周期背景上的呼吸子和怪波及其碰撞解

Abstract

Abstract:

The nonlinear Schr$\rm\ddot{o}$dinger equation is a very important integrable system in the field of physics and applied mathematics. In this paper, the breather and rogue wave on the periodic/double periodic background and the collision solutions of breather and rogue wave for the generalized derivative nonlinear Schr$\rm\ddot{o}$dinger equation are studied by using the Darboux transformation. Firstly, the Darboux transformation of the generalized derivative nonlinear Schr$\rm\ddot{o}$dinger equation is constructed. Then, by using the Darboux transformation, the breather and rogue wave on the periodic/double periodic background and the collision solutions are derived. Finally, by means of the figures, the structures of interesting new solutions are analyzed in detail, which also provide a theoretical basis for studying the physical mechanism of the new solution.

Key words: The generalized derivative nonlinear Schr?dinger equation, Darboux transformation, Periodic solution, Breather, Rogue wave

CLC Number:

0175.24

Lou Yu, Zhang Yi. Breather and Rogue Wave on the Periodic/Double Periodic Background and Interaction Solutions of the Generalized Derivative Nonlinear Schr$\rm\ddot{o}$dinger Equation[J].Acta mathematica scientia,Series A, 2024, 44(6): 1511-1519.

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Figures/Tables 7

References 29

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Breather and Rogue Wave on the Periodic/Double Periodic Background and Interaction Solutions of the Generalized Derivative Nonlinear Schr$\rm\ddot{o}$dinger Equation

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