Ioannis Giannoulis | Searcharxiv

arXiv2024

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 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.

math.DS↗

arXiv2016

Interaction of modulated gravity water waves of finite depth

We consider the capillary-gravity water-waves problem of finite depth with a flat bottom of one or two horizontal dimensions. We derive the modulation equations of leading and next-to-leading order in the hyperbolic scaling for three weakly amplitude-modulated plane-wave solutions of the linearized problem in the absence of quadratic and cubic resonances. We fully justify the derived system of macroscopic equations in the case of pure gravity waves, i.e. in the case of zero surface tension, employing the stability of the water-waves problem on the time-scale $O(1/\ep)$ obtained by Alvarez-Samaniego and Lannes.

math.AP↗