DIMACS TR: 99-38
Bifurcation of Internal Solitary Wave Modes from the Essential Spectrum
Authors: P.G. Kevrekidis and C.K.R.T. Jones
ABSTRACT
The bifurcation of internal modes from the phonon band in
models supporting solitary wave solutions has been one of
the exciting new phenomena in the field. We will present
a number of analytical and semi-analytical techniques
for the detection, study and understanding of
these modes. We will see how they appear, without threshold,
due to the discretization of the continuum equations. This perturbation
is viewed in terms of a singular continuum approximation and analyzed by both
perturbation theory and the Evans' function method. It is shown that these
methods give equivalent results. Moreover, they are corroborated by mixed
analytical-numerical computations based on the discrete Evans' function
recently developed by the first author. The extent to which these predictions
survive to strong discretizations are discussed. The results will be presented
in the context of both the sine-Gordon and the $\phi^4$ models.
Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-38.ps.gz
DIMACS Home Page