A type of multicomponent nonisospectral generalized nonlinear Schrödinger hierarchies
Jianduo Yua, Haifeng Wangb, *, and Chuanzhong Lic
aSchool of Mathematics and Statistics, Ningbo University, Ningbo, China
bSchool of Science, Jimei University, Xiamen, China
cCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China
email: *tb19080005b4@cumt.edu.cn
Received 8 December, 2022
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
DOI: 10.1134/S0040577923060077