Binary Nonlinearization of AKNS Spectral Problem under Higher-Order Symmetry Constraints

Details Binary Nonlinearization of AKNS Spectral Problem under Higher-Order Symmetry Constraints Binary Nonlinearization of AKNS Spectral Problem under Higher-Order Symmetry Constraints

1998-08-20

arxiv.org/abs/solv-int/9808010v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, latex, to appear in Chaos, Solitons and Fractals

Scientific paper

Binary nonlinearization of AKNS spectral problem is extended to the cases of higher-order symmetry constraints. The Hamiltonian structures, Lax representations, $r$-matrices and integrals of motion in involution are explicitly proposed for the resulting constrained systems in the cases of the first four orders. The obtained integrals of motion are proved to be functionally independent and thus the constrained systems are completely integrable in the Liouville sense.

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