A Vector-Product Lie Algebra of a Reductive Homogeneous Space and Its Applications

Autor:	Jian Zhou, Shiyin Zhao
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	vector-product Lie algebra integrable hierarchy vector-product identity Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 21, p 3322 (2024)
Druh dokumentu:	article
ISSN:	12213322 2227-7390
DOI:	10.3390/math12213322
Popis:	A new vector-product Lie algebra is constructed for a reductive homogeneous space, which can lead to the presentation of two corresponding loop algebras. As a result, two integrable hierarchies of evolution equations are derived from a new form of zero-curvature equation. These hierarchies can be reduced to the heat equation, a special diffusion equation, a general linear Schrödinger equation, and a nonlinear Schrödinger-type equation. Notably, one of them exhibits a pseudo-Hamiltonian structure, which is derived from a new vector-product identity proposed in this paper.
Databáze:	Directory of Open Access Journals
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