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Schemes for Generating Different Nonlinear Schrödinger Integrable Equations and Their Some Properties

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Abstract

In the paper, we want to derive a few of nonlinear Schrödinger equations with various formats and investigate their properties, such as symmetries, single soliton solutions, multi-soliton solutions, and so on. First of all, we propose an efficient and straightforward scheme for generating nonisospectral integrable hierarchies of evolution equations for which a generalized nonisospectral integrable Schrödinger hierarchy (briefly GNISH) singles out, from which we get a derivative nonlinear Schrödinger equation, a generalized nonlocal Schrödinger integrable system and furthermore we investigate the symmetries and conserved qualities of the GNISH. Next, we apply the dbar method to obtain a generalized nonlinear Schrödinger-Maxwell-Bloch (GNLS-MB) equation and its hierarchy by introducing a generalized Zakhrov-Shabat spectral problem, whose soliton solutions and gauge transformations are obtained.

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China

    Yu-feng Zhang & Hai-feng Wang

  2. School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, 221116, China

    Na Bai

Authors
  1. Yu-feng Zhang
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  2. Hai-feng Wang
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  3. Na Bai
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Correspondence to Yu-feng Zhang.

Additional information

This paper is supported by the National Natural Science Foundation of China (No.11971475).

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Zhang, Yf., Wang, Hf. & Bai, N. Schemes for Generating Different Nonlinear Schrödinger Integrable Equations and Their Some Properties. Acta Math. Appl. Sin. Engl. Ser. 38, 579–600 (2022). https://doi.org/10.1007/s10255-022-1099-z

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  • DOI: https://doi.org/10.1007/s10255-022-1099-z

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