Two-dimensional discrete solitons in rotating lattices

J Cuevas, BA Malomed and PG Kevrekidis (pdf copy 1.4 Mb)

Abstract:

We introduce a two-dimensional (2D) 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 species 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 W, a stability interval for the FSs is found in terms of lattice coupling constant C, 0<C<C_cr(R), with monotonically decreasing C_cr(R). VSs with S=1 have a stability interval, C_inf,cr^(S=1)(W)<C<C_cr^(S=1)(W), which exists for W below a certain critical value, W_cr^(S=1). This implies that S=1 VSs are destabilized in the weak coupling limit by the presence of the rotation. On the contrary, VSs with S=2, that are known to be unstable in the standard DNLS equation, with W=0, are stabilized by the rotation in region 0<C<C_cr^(S=2), with C_cr^(S=2) growing as a function of W. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by W¹0.

Phys. Rev E 76, 046608, 2007, doi:10.1103/PhysRevE.76.046608.