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A type of multicomponent nonisospectral generalized nonlinear Schrödinger hierarchies

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Abstract

We introduce a Lie algebra \(A_1\) with an arbitrary constant \(\alpha\) that can be used to solve nonisospectral problems. For a given higher-dimensional Lie algebra, we introduce two new classes of higher-dimensional Lie algebras extended by \(A_1\). By solving the extended nonisospectral zero-curvature equations that correspond to nonisospectral problems, we derive several multicomponent nonisospectral hierarchies. For one of them, with the aid of the \(Z^\varepsilon_N\)-trace identity and given the Lax pairs, we obtain the bi-Hamilton structures.

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Funding

This work was supported by the Scientific Research Start-Up Foundation of Jimei University (grant No. ZQ2022024), the Fujian Provincial Education Department (grant No. JAT220172), and the National Natural Science Foundation of China (grant No. 12071179).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, China

    Jianduo Yu

  2. School of Science, Jimei University, Xiamen, China

    Haifeng Wang

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China

    Chuanzhong Li

Authors
  1. Jianduo Yu
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  2. Haifeng Wang
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  3. Chuanzhong Li
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Correspondence to Haifeng Wang.

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Additional information

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 215, pp. 437–464 https://doi.org/10.4213/tmf10423.

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Yu, J., Wang, H. & Li, C. A type of multicomponent nonisospectral generalized nonlinear Schrödinger hierarchies. Theor Math Phys 215, 837–861 (2023). https://doi.org/10.1134/S0040577923060077

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  • DOI: https://doi.org/10.1134/S0040577923060077

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