Nonlinear interactions of solitary waves in a 2D lattice

Oscillations of a two-dimensional square lattice are considered. Interactio ns between the neighbouring particles in a basis plane only are taken into account. In the paraxial approximation of the diffraction theory. the Kadom tsev-Petviashvili (KP) evolution equation has been derived for quasiplane w aves. Collisions of some two-dimensional solitons and behaviour of multiwav e ensembles of solitary waves are considered in the framework of exact and approximate solutions of this equation. (C) 2001 Elsevier Science B.V. All rights reserved.