Soliton Theory of Two-Dimensional Lattices: The Discrete Nonlinear Schrödinger Equation

Abstract

We theoretically investigate the motion of collective excitations in the two-dimensional nonlinear Schrödinger equation with cubic nonlinearity. The form of these excitations for a broad range of parameters is derived. Their evolution and interaction is numerically studied and the modulation instability is discussed. The case of saturable nonlinearity is revisited.