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Multi-soliton solutions of a variable coefficient Schrödinger equation derived from vorticity equation

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Abstract

A variable coefficient Schrödinger equation which is derived by using the multi-scale expansion and coordinate expansion transformation method from nonlinear inviscid barotropic nondivergent vorticity equation in a \(\beta \)-plane is discussed in this paper. It is different from the previous model that the background basic flow is assumed as a function of time t. Then, the bilinear forms are obtained based on a transformation. By using the Hirota bilinear method, exact analytical solutions to the Schrödinger equation are achieved. These solutions include single-soliton, two-soliton and three-soliton solutions, whose interactions have been presented in the form of 3-d solid figure or density graphic to describe the dynamic characteristics, and might help to describe Rossby waves more suitable. Furthermore, the effects on solitons of coefficients except which relate to the dispersion relation of the model are discussed.

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Funding

This work is supported by the National Natural Science Foundation of China (12362027 and 12361069), the Inner Mongolia Autonomous Region’s Natural Science Foundation (2022QN01003), the foundational research fund in the basic sciences of Inner Mongolia Agricultural University (JC2021001), the Inner Mongolia Autonomous Region’s Program for Young Talents in Science and Technology (NJYT23099 and NMGIRT2208), the Inner Mongolia Agricultural University’s Program for Improving the Scientific Research Capability of Youth Teachers (BR220126).

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Authors and Affiliations

  1. College of Science, Inner Mongolia Agriculture University, Hohhot, 010018, China

    Liyang Xu, Xiaojun Yin, Na Cao & Shuting Bai

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  1. Liyang Xu
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  2. Xiaojun Yin
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  3. Na Cao
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  4. Shuting Bai
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L.X. helped in methodology, writing—original draft. X.Y. contributed to conceptualization, writing—reviewing and editing. N.C. was involved in validation. S.B. helped in software.

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Correspondence to Xiaojun Yin.

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Xu, L., Yin, X., Cao, N. et al. Multi-soliton solutions of a variable coefficient Schrödinger equation derived from vorticity equation. Nonlinear Dyn 112, 2197–2208 (2024). https://doi.org/10.1007/s11071-023-09158-3

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