Vortex and dipole solitons in lattices possessing defects and dislocations

Abstract

We report the numerical existence of dipole and vortex solitons for the two-dimensional nonlinear Schrödinger (NLS) equation with external potentials that possess strong irregularities, i.e., edge dislocations and a vacancy defects. Multi-humped solitons are computed by employing a spectral fixed-point computational scheme. The nonlinear stability of these solitons is investigated using direct simulations of the NLS equation and it is observed that these multi-humped modes in the defect lattices can be stable or unstable.