A new integrable symplectic map by the binary nonlinearization to the super AKNS system. (English) Zbl 1375.35438
Summary: Based on the constructed new Lie super-algebra from OSP(2,2), the super bi-Hamiltonian structure of a new super AKNS hierarchy is obtained by making use of super-trace identity. For the new super AKNS system, an explicit symmetry constraint between the potentials and the eigenfunctions is proposed. Moreover, the super AKNS system is decomposed into two compatible finite-dimensional super integrable systems and the obtained super systems are proved to be finite-dimensional super integrable Hamiltonian systems in the super-symmetry manifold \(\mathbb R^{4 N \mid 4 N} .\)
MSC:
| 35Q51 | Soliton equations |
| 37J10 | Symplectic mappings, fixed points (dynamical systems) (MSC2010) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |
Keywords:
orthosymplectic Lie superalgebras; super AKNS hierarchy; explicit symmetry constraint; binary nonlinearizationReferences:
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