Envelope solitons on two - dimensional lattices within { plane

We investigate envelope solitary waves on square with two degrees of freedom and nonlinear nearest and next-nearest neighbor interactions. We consider solitary waves which are localized in the direction of their motion and periodically modulated along the perpendicular direction. In the quasi{monochromatic approximation and low{amplitude limit a system of two coupled nonlinear Schrr odinger equations (CNLS) is obtained for the envelopes of the longitudinal and transversal displacements. For the case of bright envelope solitons the solvability condition is discussed, also with respect to the modulation. The stability of two special solution classes (type-I and type-II) of the CNLS equations is tested by molecular dynamics simulations. The shape of type-I solitary waves does not change during propagation, whereas the width of type-II exci-tations oscillates in time.