The existence of steady solutions for a class of Schrödinger equations in nonlinear optical lattices

We address the impact of nonlocality in the physical features exhibited by solitons in photorefractive optical lattice. We use the method of calculus of variations to develop an existence theory for the steady state solutions of a nonlinear Schrodinger equation modeling light waves propagating in nonlinear optical lattices. We show via a mountain-pass argument that there exist steady state solutions realizing a continuous spectrum of energy points or wavenumbers.