J. Holmer, P. G. Kevrekidis, and D. E. Pelinovsky
Orbital stability of kinks in the NLS equation with competing nonlinearities
Abstract:
Kinks connecting zero and nonzero equilibria in the NLS equation with competing
nonlinearities occur at the special values of the frequency parameter. Since they are
minimizers of energy, they are expected to be orbitally stable in the time evolution of the
NLS equation. However, the stability proof is complicated by the degeneracy of kinks near
the nonzero equilibrium. The main purpose of this work is to give a rigorous proof of the
orbital stability of kinks. We give details of analysis for the cubic–quintic NLS equation and
show how the proof is extended to the general case.
Keywords:
nonlinear Schrodinger equation; kinks; orbital stability; spectral stability;