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 $C$, $0<C<C_{\mathrm{cr}}\left(R\right)$, with monotonically decreasing $C_{\mathrm{cr}}\left(R\right)$. VSs with $S=1$ have a stability interval, ${\tilde{C}}_{\mathrm{cr}}^{(S=1)}\left(\Omega \right)<C<C_{\mathrm{cr}}^{(S=1)}\left(\Omega \right)$, which exists for $\Omega$ below a certain critical value, ${\Omega }_{\mathrm{cr}}^{(S=1)}$. 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 $0<C<C_{\mathrm{cr}}^{(S=2)}$, with $C_{\mathrm{cr}}^{(S=2)}$ growing as a function of $\Omega$. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by $\Omega \ne 0$.