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2020•Journal of Applied Analysis & ComputationOpen access

DARBOUX TRANSFORMATIONS, MULTISOLITONS, BREATHER AND ROGUE WAVE SOLUTIONS FOR A HIGHER-ORDER DISPERSIVE NONLINEAR SCHRÖDINGER EQUATION

Hongyi Zhang, Yufeng Zhang

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Abstract

In this paper, dynamic of a higher-order dispersive nonlinear Schrö-dinger equation is investigated. Firstly, we obtain the determinant representation of the N-fold Darboux transformations of the Schrödinger equation. Then based on the above analysis, we get the one-soliton, two-soliton and the breather wave solution. Furthermore, the first-order rogue wave is derived by means of a Taylor expansion of the breather wave. Finally, by selecting some special parameters and drawing the 3-D and 2-D graphs to better describe the dynamic traits of those solutions.

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What this paper is about

In this paper, dynamic of a higher-order dispersive nonlinear Schrö-dinger equation is investigated. Firstly, we obtain the determinant representation of the N-fold Darboux transformations of the Schrödinger equation. Then based on the above analysis, we get the one-soliton, two-soliton and the breather wave solution. Furthermore, the first-order rogue wave is derived by means of a Taylor expansion of the breather wave. Finally, by selecting some special parameters and drawing the 3-D and 2-D graphs to better describe the dynamic traits of those solutions.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, dynamic of a higher-order dispersive nonlinear Schrö-dinger equation is investigated. Firstly, we obtain the determinant representation of the N-fold Darboux transformations of the Schrödinger equation. Then based on the above analysis, we get the one-soliton, two-soliton and the breather wave solution. Furthermore, the first-order rogue wave is derived by means of a Taylor expansion of the breather wave. Finally, by selecting some special parameters and drawing the 3-D and 2-D graphs to better describe the dynamic traits of those solutions.

Key concepts: Breather, Rogue wave, Nonlinear Schrödinger equation, Soliton, Nonlinear system, Mathematical physics, First order, Mathematical analysis

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DARBOUX TRANSFORMATIONS, MULTISOLITONS, BREATHER AND ROGUE WAVE SOLUTIONS FOR A HIGHER-ORDER DISPERSIVE NONLINEAR SCHRÖDINGER EQUATION — Research Paper | ScholarLens