Complete eigenfunctions of linearized integrable equations expanded around an arbitrary solution

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dc.creatorYang, Jianke
dc.date2005-06-17
dc.date.accessioned2026-07-07T05:36:33Z
dc.date.available2026-07-07T05:36:33Z
dc.descriptionComplete eigenfunctions of linearized integrable equations expanded around an arbitrary solution are obtained for the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and the Korteweg-de Vries (KdV) hierarchy. It is shown that the linearization operators and the recursion operator which generates the hierarchy are commutable. Consequently, eigenfunctions of the linearization operators are precisely squared eigenfunctions of the associated eigenvalue problem. Similar results are obtained for the adjoint linearization operators as well. These results make a simple connection between the direct soliton/multi-soliton perturbation theory and the inverse-scattering based perturbation theory for these hierarchy equations.
dc.identifierhttps://arxiv.org/abs/nlin/0506037
dc.identifierhttp://arxiv.org/abs/nlin/0506037
dc.identifierStud. Appl. Math. 108, 145 (2002)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/81026
dc.subjectExactly Solvable and Integrable Systems
dc.titleComplete eigenfunctions of linearized integrable equations expanded around an arbitrary solution
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