Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector-soliton collision dynamics in nonlinear optical fibers   We consider the interactions of two identical, orthogonally polarized vector
solitons in a nonlinear optical fiber with two polarization directions,
described by a coupled pair of nonlinear Schroedinger equations. We study a
low-dimensional model system of Hamiltonian ODE derived by Ueda and Kath and
also studied by Tan and Yang. We derive a further simplified model which has
similar dynamics but is more amenable to analysis. Sufficiently fast solitons
move by each other without much interaction, but below a critical velocity the
solitons may be captured. In certain bands of initial velocities the solitons
are initially captured, but separate after passing each other twice, a
phenomenon known as the two-bounce or two-pass resonance. We derive an analytic
formula for the critical velocity. Using matched asymptotic expansions for
separatrix crossing, we determine the location of these "resonance windows."
Numerical simulations of the ODE models show they compare quite well with the
asymptotic theory.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con