P.G. Kevrekidis, D.E. Pelinovsky, and R.M. Ross
Stability of smooth solitary waves under the intensity-dependent dispersion
Abstract:
The cubic nonlinear Schrodinger equation (NLS) in one dimension is considered
in the presence of an intensity-dependent dispersion term. We study bright solitary waves
with smooth profiles which extend from the limit where the dependence of the dispersion
coecient on the wave intensity is negligible to the limit where the solitary wave becomes
singular due to vanishing dispersion coefficient. We analyze and numerically explore the
stability for such smooth solitary waves, showing with the help of numerical approximations
that the family of solitary waves becomes unstable in the intermediate region between the
two limits, while being stable in both limits. This bistability, that has also been observed in
other NLS equations with the generalized nonlinearity, brings about interesting dynamical
transitions from one stable branch to another stable branch, that are explored in direct
numerical simulations of the NLS equation with the intensity-dependent dispersion term.
Keywords:
nonlinear Schrodinger equation, intensity-dependent dispersion, bright solitary waves,
energetic stability.