Binary nonlinearization of AKNS spectral problem under higher-order symmetry constraints
نویسندگان
چکیده
منابع مشابه
Binary Nonlinearization of AKNS Spectral Problem under Higher-Order Symmetry Constraints
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 th...
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The method of nonlinearization of Lax pair for the classical integrable (1+1)-dimensional system has aroused strong interests in soliton theory, including mono-nonlinearization [1, 2, 3] and binary nonlinearization [4, 5]. The crucial technique is to find constraints between the potentials (i. e, functions of soliton equation) and the eigenfunctions of the spectral problem associated with the s...
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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 ...
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Adjoint symmetry constraints are presented to manipulate binary nonlinearization, and shown to be a slight weaker condition than symmetry constraints in the case of Hamiltonian systems. Applications to the multicomponent AKNS system of nonlinear Schrödinger equations and the multi-wave interaction equations, associated with 3×3 matrix spectral problems, are made for establishing their integrabl...
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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...
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ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 2000
ISSN: 0960-0779
DOI: 10.1016/s0960-0779(98)00173-8