Solitons in Gaussian potential with spatially modulated nonlinearity

We investigated theoretically the existence, stability and propagation dynamics of fundamental and dipole solitons in the potential featuring locally Gaussian modulation of linear refractive index and out-of-phase nonlinearity. Fundamental solitons are stable in the moderate power region and the stability window shrinks with the depth of nonlinearity modulation, while there exist several discrete narrow stable windows for the dipole solitons. Also, a power-dependent shape transformation is found in the high power region for deep enough nonlinear modulation. The transverse mobility of solitons launched with a tilt angle was also discussed, and the results show the critical tilt angles for soliton deflecting from the channel increase with a decrease of the propagation constant. For the low energy soliton, only part of the soliton would keep oscillating in the channel and the other part would deflect away even if the tilt angle is smaller than the critical value.