Title: Analytical approximations to discrete soliton profiles in DNLS models

Author: J Cuevas (pdf slides 996 Kb and proceedings).
With PG Kevrekidis, BA Malomed and B Sánchez-Rey

Abstract: In this talk, we show two approximate methods for calculating, analytically, the profile of discrete solitons in the Discrete Nonlinear Schr¨odinger (DNLS) equation. One method consists in a variational calculation of the amplitude of the soliton, supposing that it has a peaked spatial profile. To this end, we use a modification of the methods presented in [1]. The other method is based in the assumption that discrete solitons in the DNLS can be homoclinic orbits in a two-dimensional map [2]. Our contribution to this method consists in approximating the homoclinic orbits by a polynomial form.

[1] B.A. Malomed and M.I. Weinstein. Soliton dynamics in the DNLS equation. Physics Letters A, 220 (1996) 91.

[2] D. Hennig, K.O. Rasmussen, H. Gabriel and A. Bülow. Solitonlike solutions of the generalized DNLS equation. Physical Review E, 54 (1996) 5788.

Nonlinear evolution equations and dynamical systems 2007, L'Ametlla de Mar (Tarragona - Spain), June 16-23, 2007.
Talk by J Cuevas.