The semidirect sum of Lie algebras and its applications to C-KdV hierarchy. (English) Zbl 1449.37048

Summary: By use of the loop algebra \(\overset\simeq G\), integrable coupling of C-KdV hierarchy and its bi-Hamiltonian structures are obtained by G. Tu scheme [J. Math. Phys. 30, No. 2, 330–338 (1989; Zbl 0678.70015)] and the quadratic-form identity. The method can be used to produce the integrable coupling and its Hamiltonian structures to the other integrable systems.


37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K06 General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws
17B80 Applications of Lie algebras and superalgebras to integrable systems


Zbl 0678.70015
Full Text: DOI


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