Abstract
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.
Subject
General Earth and Planetary Sciences,General Energy
Reference11 articles.
1. Lax, P.D. Integrals of nonlinear equations of evolution and solitary waves / P.D. Lax // Comm. Pure Appl. Math. – 1968. – Vol. 21. – P. 467., Lax, P.D. Integrals of nonlinear equations of evolution and solitary waves / P.D. Lax // Comm. Pure Appl. Math. – 1968. – Vol. 21. – P. 467.
2. Gardner, C.S. Method for solving the Korteweg-deVries equation / C.S. Gardner, J. Green, M. Kruskal, R. Miura // Phys. Rev. Lett. – 1967. – Yol. 19. P. 1095., Gardner, C.S. Method for solving the Korteweg-deVries equation / C.S. Gardner, J. Green, M. Kruskal, R. Miura // Phys. Rev. Lett. – 1967. – Yol. 19. P. 1095.
3. Захаров, В.Е. Точная теория двумерной самофокусировки и одномерной самомодуляции волн в нелинейных средах / В.Е. Захаров, А.Б. Шабат // ЖЭТФ. – 1972. – Т. 61, № 1. – С. 118., Zaharov, V.E. Tochnaya teoriya dvumernoy samofokusirovki i odnomernoy samomodulyacii voln v nelineynyh sredah / V.E. Zaharov, A.B. Shabat // ZhETF. – 1972. – T. 61, № 1. – S. 118.
4. Ablowitz, M.J. Solitons and inverse scattering transform / M.J. Ablowitz, H. Segur. – Philadelphia: SIAM, 1981 – P. 435., Ablowitz, M.J. Solitons and inverse scattering transform / M.J. Ablowitz, H. Segur. – Philadelphia: SIAM, 1981 – P. 435.
5. Лезнов, A.Н. Групповые методы интегрирования нелинейных динамических систем / A.Н. Лезнов, M.В. Савельев. – Москва: Наука, Гл. ред. физ.-мат. лит., 1985. – 279 с., Leznov, A.N. Gruppovye metody integrirovaniya nelineynyh dinamicheskih sistem / A.N. Leznov, M.V. Savel'ev. – Moskva: Nauka, Gl. red. fiz.-mat. lit., 1985. – 279 s.
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1. Lax equations on Lie superalgebras;Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences;2024-08-07