Tensor extensions of Lax equations
Автор: Karabanov A.
Журнал: Известия Коми научного центра УрО РАН @izvestia-komisc
Рубрика: Научные статьи
Статья в выпуске: 4 (62), 2023 года.
Бесплатный доступ
The Lax equations dL/dt = [M,L] play an important role in the integrability theory of nonlinear evolution equations and quantum dynamics. In this work, tensor extensions of the Lax equations are suggested with M : V → V and L : Tk(V ) → V , k = 1, 2, . . ., on a complex vector space V . These extensions belong to the generalised class of Lax equations (introduced earlier by Bordemann) dL/dt = ρk(M)L where ρk is a representation of a Lie algebra. The case k = 1, ρ1 = ad corresponds to the usual Lax equations. The extended Lax pairs are studied from the point of view of isomorphic deformations of multilinear structures, conservation laws, exterior algebras and cochain symmetries.
Lax equations, tensor extensions, multilinear algebra, symmetries
Короткий адрес: https://sciup.org/149143595
IDR: 149143595 | DOI: 10.19110/1994-5655-2023-4-5-9
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