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 Omega , a stability interval for the FSs is found in terms of the lattice coupling constant C , 0<C<C_{cr}(R) , with monotonically decreasing C_{cr}(R) . VSs with S=1 have a stability interval, C[over ]_{cr};{(S=1)}(Omega)<C<C_{cr};{(S=1)}(Omega) , which exists for Omega below a certain critical value, Omega_{cr};{(S=1)} . 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 Omega=0 , are stabilized by the rotation in region 0<C<C_{cr};{(S=2)} , with C_{cr};{(S=2)} growing as a function of Omega . Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by Omega not equal 0 .