Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations

Details Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations

2003-02-17

arxiv.org/abs/math/0302197v1

Mathematics

Analysis of PDEs

Nonlinear Dynamics (in press)

Scientific paper

In 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.

Affiliated with

Also associated with

No associations

Rating

Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-501791