This article is cited in 4 papers

A type of multicomponent nonisospectral generalized nonlinear Schrödinger hierarchies

Jianduo Yu^a, HaiFeng Wang^b, Chuanzhong Li<sup>c

a</sup> School of Mathematics and Statistics, Ningbo University, Ningbo, China
^b School of Science, Jimei University, Xiamen, China
^c College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China

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.

Keywords: multicomponent nonisospectral hierarchy, $Z^\varepsilon_N$-trace identity, bi-Hamiltonian structure, nonisospectral problem.

MSC: 35Q55, 37K30

Received: 08.12.2022
Revised: 08.12.2022

DOI: 10.4213/tmf10423

 English version: Theoretical and Mathematical Physics, 2023, 215:3, 837–861

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