Vortex and dipole solitons in complex two-dimensional nonlinear lattices

Using computational methods, it is found that the two-dimensional nonlinear Schrödinger (NLS) equation with a quasicrystal lattice potential admits multiple dipole and vortex solitons. The linear and the nonlinear stability of these solitons is investigated using direct simulations of the NLS equation and its linearized equation. It is shown that certain multiple vortex structures on quasicrystal lattices can be linearly unstable but nonlinearly stable. These results have application to investigations of localized structures in nonlinear optics and Bose-Einstein condensates.