Combined Envelope-Envelope solitons on square lattices

Roland Huß

Institut für Theoretische Physik, Universität Bayreuth, D-95440 Bayreuth, Germany

A square lattice with nonlinear interactions between nearest and next-nearest neighbours is considered. These interactions are described by potentials in form of a series up to fourth order in the relative displacements. In a previous work [1] we demonstrated the existence of a combined state of a pulse and envelope solitary wave for the longitudinal and transversal displacement respectively. These excitations depend solely on one space variable. In this work we extend this approach by looking for structures which depend on both space directions. We consider localization in the longitudinal direction while in the transversal direction a periodic modulation is applied. Numerical simulations indicate the possibility of long-lived excitations of this kind, where both displacement fields are envelope structures along the longitudinal direction. The results of the simulations and some hints for an analytical investigation are presented.

Reference :

[1]

R. Huß, F.G. Mertens and Y. Gaididei. Pulse-envelope solitons on 2-d lattices with in-plane displacements. In A.R. Bishop, S. Jiménez, and L. Vázquez, editors, Fluctuation Phenomena : Disorder and Nonlinearity, Singapore. World Scientific. in press.