Analysis Seminar

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On-Site and Off-Site Solitary Waves of the Discrete Nonlinear Schrödinger Equation in Multiple Dimensions

Speaker: Michael Jenkinson, Columbia University

Location: Warren Weaver Hall 1302

Date: Thursday, October 23, 2014, 11 a.m.

Synopsis:

We construct several families of symmetric localized standing waves (solitons) to the one-, two-, and three-dimensional discrete nonlinear Schrödinger equation (DNLS) with cubic nonlinearity using bifurcation methods about the continuum limit. Such waves and their energy differences play a role in the propagation of localized states of DNLS across the lattice. The energy differences, which we prove to exponentially small in a natural parameter, are related to the "Peierls-Nabarro Barrier" in discrete systems, first investigated by M. Peyrard and M.D. Kruskal (1984). These results may be generalized to different lattice geometries and inter-site coupling parameters. This is joint work with Michael I. Weinstein.