Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations

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dc.creatorLi, Yanguang Charles
dc.date2003-02-17
dc.date.accessioned2026-07-07T04:55:21Z
dc.date.available2026-07-07T04:55:21Z
dc.descriptionIn this paper, we study the discrete cubic nonlinear Schroedinger lattice under Hamiltonian perturbations. First we develop a complete isospectral theory relevant to the hyperbolic structures of the lattice without perturbations. In particular, Backlund-Darboux transformations are utilized to generate heteroclinic orbits and Melnikov vectors. Then we give coordinate-expressions for persistent invariant manifolds and Fenichel fibers for the perturbed lattice. Finally based upon the above machinery, existence of codimension 2 transversal homoclinic tubes is established through a Melnikov type calculation and an implicit function argument. We also discuss symbolic dynamics of invariant tubes each of which consists of a doubly infinite sequence of curve segments when the lattice is four dimensional. Structures inside the asymptotic manifolds of the transversal homoclinic tubes are studied, special orbits, in particular homoclinic orbits and heteroclinic orbits when the lattice is four dimensional, are studied.
dc.descriptionNonlinear Dynamics (in press)
dc.identifierhttps://arxiv.org/abs/math/0302197
dc.identifierhttp://arxiv.org/abs/math/0302197
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66546
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subject35; 37
dc.titleHomoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations
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