Kinks in NLS models with competing nonlinearities

Kinks connecting zero and nonzero equilibria in the NLS equation with competing nonlinearities occur at the special values of frequency. Since they are minimizers of energy, they are expected to be orbitally stable in the evolution of the NLS equation. However, the stability proof is complicated by the degeneracy of kinks near the nonzero equilibrium. I will give details of analysis and computations for the cubic-quintic NLS equation and show how the proof is extended to the general case. I will also discuss persistence of kinks in the lattice models.

Bio
https://pelinovsky.mcmaster.ca/