Modulation Instability Analysis, Solitary Wave Solutions, Dark Soliton Solutions, and Complexitons for the (3 + 1)-Dimensional Nonlinear Schrödinger Equation

Chun-Yan Qin and Kenan Yildirim

Journal of Mathematics, 2022, vol. 2022, 1-8

Abstract: This paper addresses the (3 + 1)-dimensional nonlinear Schrödinger equation, which could be utilized to express many physical media the envelope of the wave amplitude. With the help of He’s semi-inverse method, the solitary wave solutions are explicitly constructed to the equation. The dark soliton solutions of the equation are also strictly constructed by making use of the solitary ansatz method; in order to guarantee the existence of solitons, some conditions are given. Furthermore, by employing the tanh  method, we also present complexitons of the equation. Finally, with the aid of linear stability analysis, an effective and straightforward method is presented to analyze modulation instability of the equation.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4689857

DOI: 10.1155/2022/4689857

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