Eur. Phys. J. B 6, 257-271 (1998)
https://doi.org/10.1007/s100510050548

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

¹ Institute for Theoretical Physics, 252143 Kiev, Ukraine
² Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany

Corresponding author: ^a franz.mertens@theo.phy.uni-bayreuth.de

Received: 4 December 1997
Revised: 6 June 1998
Accepted: 7 July 1998
Published online: 15 November 1998

Abstract

We investigate envelope solitary waves on square lattices 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 Schrödinger equations (CNLS) is obtained for the envelopes of the longitudinal and transversal displacements. For the case of bright envelope solitary waves 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 excitations oscillates in time.