Geodesic
A~type of multicomponent nonisospectral generalized nonlinear Schr\"{o}dinger hierarchies
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 3, pp. 437-464

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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. 
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     author = {Jianduo Yu and HaiFeng Wang and Chuanzhong Li},
     title = {A~type of multicomponent nonisospectral generalized nonlinear {Schr\"{o}dinger} hierarchies},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {215},
     number = {3},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2023_215_3_a6/}
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Jianduo Yu; HaiFeng Wang; Chuanzhong Li. A~type of multicomponent nonisospectral generalized nonlinear Schr\"{o}dinger hierarchies. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 3, pp. 437-464. http://geodesic.mathdoc.fr/item/TMF_2023_215_3_a6/