Volume 17, Issue 3, September 2010, Pages 357 - 377
Discrete Multiscale Analysis: A Biatomic Lattice System
Authors
G. A. Cassatella Contra*, D. Levi†
*Departamento de Física Teórica II, (Métodos Matemáticos de la Física), Universidad Complutense de Madrid, Ciudad Universitaria, 28040 — Madrid, Spain
†Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre and Sezione, INFN Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
Received 26 October 2009, Accepted 13 July 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000957How to use a DOI?
- Keywords
- Multiple scale expansions; asymptotic analysis on the lattice; integrable equations; nonlinear chains; discrete Nonlinear Schrödinger equation; biatomic lattices
- Abstract
We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations.
We require that also the reduced equation be discrete. To do so coherently we need to discretize the time variable to be able to get asymptotic discrete waves and carry out a discrete multiscale expansion around them. Our resulting nonlinear equation will be a kind of discrete Nonlinear Schrödinger equation. If we make its continuum limit, we obtain the standard Nonlinear Schrödinger differential equation.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - G. A. Cassatella Contra AU - D. Levi PY - 2021 DA - 2021/01/07 TI - Discrete Multiscale Analysis: A Biatomic Lattice System JO - Journal of Nonlinear Mathematical Physics SP - 357 EP - 377 VL - 17 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000957 DO - 10.1142/S1402925110000957 ID - CassatellaContra2021 ER -