Spatial solitons with complicated structure in nonlocal nonlinear media

In nonlocal nonlinear media with a sine-oscillation response function, two kinds of spatial solitons with complicated structure, in-phase and out-of-phase bound-state solitons, are obtained numerically in the case of the weak nonlocality. The in-phase bound-state soliton exhibits the symmetrical profile and the nonzero central value, and the out-of-phase bound-state soliton has the antisymmetrical profile and the zero central value. The two kinds of bound-state solitons form the degenerate modes subject to the same dependance of soliton power on the propagation constant. For those solitons there exist two abnormal properties: both the soliton propagation constants and the slope of the power versus propagation constants are negative. Both the in-phase and the out-of-phase bound-state solitons are stable by the linear stability analysis, and the stability of the two kinds of solitons obey an inverted Vakhitov-Kolokolov stability criterion. We also discuss the way how to obtain a set of the soliton solutions from one numerical soliton solution via the transform invariance of the nonlocal nonlinear Schrodinger equation and the nonlinear Schrodinger equation.