Collapse arrest for two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam in nonlocal nonlinear media

Propagation dynamics of two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam are investigated numerically in local and nonlocal nonlinear media. The self-healing and collapse of the beam depend crucially on the distribution factor $b$ and the topological charge $m$. With the help of nonlocality, stable Airy Gaussian beam and Airy Gaussian vortex beam with larger amplitude can be obtained, which always collapse in local nonlinear media. When the distribution factor $b$ is large enough, the Airy Gaussian vortex beam will transfer into quasi-vortex solitons in nonlocal nonlinear media.

Stable high dimensional solitons in nonlocal competing cubic-quintic nonlinear media

We find and stabilize high dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media. By adjusting the propagation constant, cubic and quintic nonlinear coefficients, the stable intervals for dipole and quadrupole solitons which are parallel to $x$ axis and ones after rotating 45 degrees counterclockwise around the origin of coordinate are found. For the dipole solitons and ones after rotating, their stability is controlled by the propagation constant, the coefficients of cubic and quintic nonlinearity. For the quadrupole solitons, their stability is controlled by the propagation constant and the coefficient of cubic nonlinearity, rather than the coefficient of quintic nonlinearity, though there is a small effect of the quintic nonlinear coefficient on the stability. Our proposal may provide a way to generate and stabilize some novel high dimensional nonlinear modes in nonlocal system.