Classification of solutions of the generalized mixed nonlinear Schrödinger equation

Deqin Qiu^a, Yongshuai Zhang<sup>b

a</sup> Department of Mathematics, School of Science, China University of Mining and Technology, Beijing, China
^b School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, China

Abstract: We construct a generalized Darboux transformation for a generalized mixed nonlinear Schrödinger equation and consider a complete reduction classification of parameters and eigenfunctions of the two-, three-, and four-fold generalized Darboux transformations. According to these different types of reductions, several solutions of the generalized mixed nonlinear Schrödinger equation are found, including a soliton, a quasirational soliton, and a periodic soliton. Finally, a classification corresponding to these reductions is given.

Keywords: generalized mixed nonlinear Schrödinger equation, generalized Darboux transformation, soliton solution.

MSC: 35Q51,37K40

Received: 17.11.2021
Revised: 04.01.2022

DOI: 10.4213/tmf10199

 English version: Theoretical and Mathematical Physics, 2022, 211:3, 838–855

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