Localized non-linear modes, or solitons, were obtained for the two-dimensional non-linear Schrödinger equation with various external potentials that possess large variations from periodicity, i.e., vacancy defects, edge dislocations, and quasicrystal structure. The solitons were obtained by employing a spectral fixed-point computational scheme. Investigation of soliton evolution by direct numerical simulations showed that irregular-lattice solitons could be stable, unstable, or undergo collapse.

Solitons in Two-Dimensional Lattices Possessing Defects, Dislocations and Quasicrystal Structures. M.J.Ablowitz, B.Ilan, E.Schonbrun, R.Piestun: Physical Review E, 2006, 74[3], 035601 (4pp)