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Nonlinear continuous integrable Hamiltonian couplings. (English) Zbl 1234.37047
In this paper, a scheme is established to construct nonlinear continuous integrable couplings by means of a kind of special non-semisimple matrix Lie algebras. Variational identities over the associated loop algebras are used to build Hamiltonian structures for the resulting couplings. The AKNS hierarchy of soliton equations is used to give an example of application of the scheme.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35A30 Geometric theory, characteristics, transformations in context of PDEs
35F50 Systems of nonlinear first-order PDEs
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
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