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

2024/01/26 by Ioannis Giannoulis, Bernd Schmidt, Giannoulis, Ioannis +3
Engineering · Physics and Astronomy · #35Q55 #35Q70 #37K60 #Advanced Fiber Optic Sensors #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mechanical and Optical Resonators #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.2401.14947

openalex publication_date 2024/01/26 · openalex created_date 2024/01/30 · openalex updated_date 2026/07/28

Abstract

We consider a scalar Fermi-Pasta-Ulam-Tsingou (FPUT) system on a square 2D lattice with a cubic nonlinearity. For such systems the 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.

Related

• KP-II approximation for a scalar FPU system on a 2D square lattice
• Lattice Approximations to NLS
• Long-Time approximations of small-amplitude, long-wavelength FPUT solutions
• Approximation of (some) FPUT lattices by KdV Equations
• Using Random Walks to Establish Wavelike Behavior in an FPUT System with Random Coefficients