NLS approximation for a scalar FPUT system on a 2D square lattice with a cubic nonlinearity

We consider a scalar Fermi-Pasta-Ulam-Tsingou (FPUT) system on a square 2D lattice with a cubic nonlinearity. For such systems the nonlinear Schrödinger (NLS) equation can be derived to describe the evolution of an oscillating moving wave packet of small amplitude which is slowly modulated in time a...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-12, Vol.540 (2), p.128625, Article 128625
Main Authors: Giannoulis, Ioannis, Schmidt, Bernd, Schneider, Guido
Format: Article
Language:English
Subjects:
FPUT system
Modulation equations
Multi-dimensional nonlinear lattices
Multiple scales
NLS equation
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Summary:We consider a scalar Fermi-Pasta-Ulam-Tsingou (FPUT) system on a square 2D lattice with a cubic nonlinearity. For such systems the nonlinear Schrödinger (NLS) equation can be derived to describe the evolution of an oscillating moving wave packet of small amplitude which is slowly modulated in time and space. We show that this NLS approximation makes correct predictions about the dynamics of the original scalar FPUT system for the strain and the displacement variables. The present paper provides the first NLS approximation result for a 2D lattice in a full Galilean invariant setting without imposing an on-site potential.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128625