2009/02/11 by Johannes Giannoulis, Giannoulis, Johannes
Computer Science · Mathematics · Physics and Astronomy · #34C20 #34E13 #35L45 #35L60 #37K60 #70F45 #70K70 #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP #msc:34C20 #msc:34E13 #msc:35L45 #msc:35L60 #msc:37K60 #msc:70F45 #msc:70K70
paper · pdf · doi:10.48550/arxiv.0902.1776
41 pages
arxiv created 2009/02/11 · openalex publication_date 2009/02/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the macroscopic dynamics of sets of an arbitrary finite number of weakly amplitude-modulated pulses in a multidimensional lattice of particles. The latter are assumed to exhibit scalar displacement under pairwise, arbitrary-range, nonlinear interaction potentials and are embedded in a nonlinear background field. By an appropriate multiscale ansatz, we derive formally the explicit evolution equations for the macroscopic amplitudes up to an arbitrarily high order of the scaling parameter, thereby deducing the resonance and non-resonance conditions on the fixed wave vectors and frequencies of the pulses, which are required for that. The derived equations are justified rigorously in time intervals of macroscopic length. Finally, for sets up to three pulses we present a complete list of all possible interactions and discuss their ramifications for the corresponding, explicitly given macroscopic systems.