Envelope solitary waves on two-dimensional lattices with in-plane displacements

We investigate envelope solitary waves on square lattices with two degrees of freedom and nonlinear nearest and nest-nearest neighbor interactions. We consider solitary waves which are localized in the direction of their moti on and periodically modulated along the perpendicular direction. In the qua simonochromatic approximation and low-amplitude limit a system of two coupl ed nonlinear Schrodinger equations (CNLS) is obtained for the envelopes of the longitudinal and transversal displacements. For the case of bright enve lope solitary waves thp solvability condition is discussed, also with respe ct to the modulation. The stability of two special solution classes (type-I and type-II) of the CNLS equations is tested by molecular dynamics simulat ions. The shape of type-I solitary waves does not change during propagation , whereas the width of type-II excitations oscillates in time.