Fundamental, Dipole and Vortex Solitons in Complex 2D Nonlinear Lattices

Fundamental, Dipole and Vortex Solitons in Complex 2D Nonlinear Lattices

Nalan Antar
Department of Mathematics
Istanbul Technical University

Band gap formation and fundamental solitons in two the dimensional (2+1)D nonlinear Schröodinger (NLS) equation with external potentials (lattices) possessing crystal and quasicrystal structures are studied. The fundamental solitons are obtained by using a spectral fixed-point numerical scheme. Band gap structures are obtained numerically for these irregular type lattices. Nonlinear and linear stability properties of fundamental solitons are investigated by direct simulation and the linear stability properties of the fundamental solitons are confirmed by analysis the linearized eigenvalue problem. The existence of vortex solitons are demonstrated numerically in the semi-infinite gap of the focusing two-dimensional NLS equation under kerr and saturable nonlinearity in periodic and the Penrose potentials. We use a spectral fixed-point computational scheme to obtain the vortex solitons. Nonlinear and linear stability properties of the vortex solitons are investigated by direct simulations and the linear stability properties of the vortex solitons are confirmed by analysis the linearized eigenvalue problem.