Two-dimensional discrete solitons in rotating lattices

Abstract

We introduce a two-dimensional discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two types of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance R from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities S=1 and 2. At a fixed value of rotation frequency Ω, a stability interval for the FSs is found in terms of the lattice coupling constant C, 0<C<Ccr(R), with monotonically decreasing Ccr(R). VSs with S=1 have a stability interval, C̃ (S=1)cr(Ω)<C<C(S=1)cr(Ω), which exists for Ω below a certain critical value, Ω(S=1)cr. This implies that the VSs with S=1 are destabilized in the weak-coupling limit by the rotation. On the contrary, VSs with S=2, that are known to be unstable in the standard DNLS equation, with Ω=0, are stabilized by the rotation in region 0<C<C(S=2)cr, with C(S=2)cr growing as a function of Ω. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by Ω≠0.