Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under
  Hamiltonian Perturbations   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.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga