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Wang, Lei; Tang, Ya-Ning

Tri-integrable couplings of the Giachetti-Johnson soliton hierarchy as well as their Hamiltonian structure. (English) Zbl 1474.37087

Abstr. Appl. Anal. 2014, Article ID 627924, 8 p. (2014).
Summary: Based on zero curvature equations from semidirect sums of Lie algebras, we construct tri-integrable couplings of the Giachetti-Johnson (GJ) hierarchy of soliton equations and establish Hamiltonian structures of the resulting tri-integrable couplings by the variational identity.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
17B80 Applications of Lie algebras and superalgebras to integrable systems
35Q51 Soliton equations
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
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\textit{L. Wang} and \textit{Y.-N. Tang}, Abstr. Appl. Anal. 2014, Article ID 627924, 8 p. (2014; Zbl 1474.37087)
Full Text: DOI

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