RH Goodman, PJ Holmes, MI Weinstein
Strong NLS Soliton-Defect Interactions
(460K, Latex 2e with many postscript figures)

ABSTRACT.  We consider the interaction of a nonlinear Schr\"odinger soliton with 
a spatially localized (point) defect in the medium through which it 
travels. Using numerical simulations, we find parameter regimes under 
which the soliton may be reflected, transmitted, or captured by the 
defect. We propose a mechanism of resonant energy transfer to a 
nonlinear standing wave mode supported by the defect. Extending 
Forinash et.\ al.~\cite{FPM:94}, we then derive a finite-dimensional model 
for the interaction of the soliton with the defect via a collective 
coordinates method. The resulting system is a three degree-of-freedom 
Hamiltonian with an additional conserved quantity. We study this 
system both numerically and using the tools of dynamical systems 
theory, and find that it exhibits a variety of interesting behaviors, 
largely determined by the structures of stable and unstable manifolds 
of special classes of periodic orbits. We use this geometrical 
understanding to interpret the simulations of the finite-dimensional 
model, compare them with the nonlinear Schr\"odinger simulations, and 
comment on differences due to the finite-dimensional ansatz. 
To fit into the archive's file size requirements, low-resolution 
versions of certain large figures were used. A version of this paper with the 
full figures is available http://m.njit.edu/~goodman/