Binary Nonlinearization of Lax Pairs
نویسنده
چکیده
A kind of Bargmann symmetry constraints involved in 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 Hamil-tonian 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.
منابع مشابه
Binary Nonlinearization for the Dirac Systems*
A Bargmann symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the Dirac systems. It is shown that the spatial part of the nonlinearized Lax pairs and adjoint Lax pairs is a finite dimensional Liouville integrable Hamiltonian system and that under the control of the spatial part, the time parts of the nonlinearized Lax pairs and adjoint Lax pairs are interpreted as a ...
متن کاملar X iv : s ol v - in t / 9 60 80 03 v 1 6 A ug 1 99 6 Binary Nonlinearization of Lax pairs of Kaup - Newell Soliton Hierarchy
— Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense,...
متن کاملA 3 3 Matrix Spectral Problem for Akns Hierarchy and Its Binary Nonlinearization
A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess classical Hamiltonian structures, in which the nonlinearized spatial system is intimately related to stationary AKNS ows. These nonlin-earized Lax systems also ...
متن کاملAKNS hierarchy and its binary Nonlinearization
A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess classical Hamiltonian structures, in which the nonlinearized spatial system is intimately related to stationary AKNS flows. These nonlinearized Lax systems also...
متن کاملThe Bargmann Symmetry Constraint and Binary Nonlinearization of the Super Dirac Systems∗∗∗∗∗
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the supersymmetry manifold R4N|2N with the corresponding dynamical v...
متن کامل