Binary Nonlinearization of Lax Pairs

Details Binary Nonlinearization of Lax Pairs Binary Nonlinearization of Lax Pairs

1996-05-31

arxiv.org/abs/solv-int/9605009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

8 pages, latex, to appear in the Proceedings of Nonlinear Physics, Italy

Scientific paper

A kind of Bargmann symmetry constraints involving Lax pairs and adjoint Lax pairs is proposed for soliton hierarchy. The Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative finite dimensional integrable Hamiltonian systems and explicit integrals of motion may also be generated. The corresponding binary nonlinearization procedure leads to a sort of involutive solutions to every system in soliton hierarchy which are all of finite gap. An illustrative example is given in the case of AKNS soliton hierarchy.

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