Binary nonlinearization of spectral problems of the perturbation AKNS systems |
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| Institution: | 1. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, PR China;2. Department of Mathematics, Xuzhou Normal University, Xuzhou 221009, PR China;1. Department of Cardiovascular Surgery, University of Oxford, John Radcliffe Hospital, Oxford, United Kingdom;2. Department of Cardiac Surgery, Oxford University Hospitals Trust, Oxford, United Kingdom;1. School of Physics, Northwest University, Xi''an, 710127, China;2. Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi''an 710127, China;3. Institute of Modern Physics, Northwest University, Xi''an 710127, China;1. Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, United States;2. Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada |
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| Abstract: | The method of nonlinearization of spectral problems is extended to the perturbation AKNS systems, and a new kind of finite-dimensional Hamiltonian systems is obtained. It is shown that the obtained Hamiltonian systems are just the perturbation systems of the well-known constrained AKNS flows and thus their Liouville integrability is established by restoring from the Liouville integrability of the constrained AKNS flows. As a byproduct, the process of binary nonlinearization of spectral problems and the process of perturbation of soliton equations commute in the case of the AKNS hierarchy. |
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