Based on the division Fourier algorithm and the rapid virtual time evolution (AITEM) iterative method, the transmission characteristics of bullet in linear and nonlinear scattering out of phase modulation Kummer-Gauss optical lattice are studied. The results show that the linear and nonlinear phase modulation significantly change the bullet shape and its range of stability, and the nonlinear modulation depth through the propagation constant controls the stability region width. It is shown that stable space-time soliton energy will grow with nonlinear modulation depth strengthening.

We solve the two-dimensional strongly nonlocal nonlinear Schrdinger equation in polar coordinates. An exact analytical solution of self-similar waves, namely Kummer-Gaussian soliton clusters, is obtained. Numerical simulations confirm the validity of the analytical solutions. It is shown that the nonlocal optical spacial solitons have large phase shift.

The F-expansion technique and the homogeneous nonlinear balance principle have been applied for solving a general (1+1)-dimensional nonlinear Schrödinger equation (NLSE) with varying coefficients and a harmonic potential. A family of (1+1)D spatial solitons has been obtained. The evolution features of exact solutions have been investigated.