Two-dimensional discrete solitons in rotating lattices

We introduce a two-dimensional discrete nonlinear Schrodinger (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 tilde ((S=1))(cr)(Omega)< C < C-cr((S=1))(Omega), which exists for Omega below a certain critical value, Omega((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 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.