Generation of higher-dimensional isospectral-nonisospectral integrable hierarchies associated with a~new class of higher-dimensional column-vector loop algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 221-248
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We construct a new class of higher-dimensional column-vector loop algebras. Based on it, a method for generating higher-dimensional isospectral–nonisospectral integrable hierarchies is proposed. As an application, we derive a generalized nonisospectral integrable Schrödinger hierarchy that can be reduced to the famous derivative nonlinear Schrödinger equation. By using the higher-dimensional column-vector loop algebras, we obtain an extended isospectral–nonisospectral integrable Schrödinger hierarchy that can be reduced to many classical and new equations, such as the extended nonisospectral derivative nonlinear Schrödinger system, the heat equation, and the Fokker–Planck equation, which has a wide range of applications in stochastic dynamical systems. Furthermore, we deduce a $Z_N^\varepsilon$ nonisospectral integrable Schrödinger hierarchy, which means that the coupling results are extended to an arbitrary number of components. Additionally, the Hamiltonian structures of these hierarchies are discussed by using the quadratic form trace identity.
Keywords:
generalized integrable Schrödinger hierarchies, higher-dimensional isospectral–nonisospectral integrable hierarchies, higher-dimensional column-vector loop algebras, Hamiltonian structure.
@article{TMF_2024_219_2_a2,
author = {Haifeng Wang and Yufeng Zhang},
title = {Generation of higher-dimensional isospectral-nonisospectral integrable hierarchies associated with a~new class of higher-dimensional column-vector loop algebra},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {221--248},
publisher = {mathdoc},
volume = {219},
number = {2},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a2/}
}
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Haifeng Wang; Yufeng Zhang. Generation of higher-dimensional isospectral-nonisospectral integrable hierarchies associated with a~new class of higher-dimensional column-vector loop algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 221-248. http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a2/