|
Organizers |
Reduction of effective Hamiltonian structures for interacting pulses in nonlinear lattices
by
Johannes Giannoulis
Zentrum Mathematik, TU München
Coauthors: M. Herrmann, HU zu Berlin, A. Mielke, WIAS Berlin and HU zu Berlin
Given N pulses in a nonlinear lattice modeled as N amplitude-modulated plane-wave solutions of the linearized system with small amplitudes eAi, i=1, ..., N, 0 < e << 1, which vary on a much longer time and space scale than the one of the original microscopic lattice, one can derive the macroscopic modulation equations governing the evolution of the amplitudes Ai by inserting their linear-combination ansatz into the microscopic system. However, this procedure ignores the underlying Hamiltonian structure of the microscopic lattice as well as the one of the obtained macroscopic system. Thus, the question arises how these Hamiltonian structures are related to each other and whether one can derive the latter directly from the former. In the present talk we address this question by applying on the example of three interacting pulses in a nonlinear Klein-Gordon-type oscillator chain a general approach for the direct reduction of effective Lagrangian and Hamiltonian structures for discrete Hamiltonian lattices.
Date received: July 3, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavj-78.