D.E. Pelinovsky and G. Schneider
KP-II approximation for a scalar FPU system on a 2D square lattice
SIAM J. Appl. Math. 83 (2023) 79-98
Abstract:
We consider a scalar Fermi-Pasta-Ulam (FPU) system on a square 2D lattice.
The Kadomtsev-Petviashvili (KP-II) equation can be derived by means of multiple scale
expansions to describe unidirectional long waves of small amplitude with slowly varying
transverse modulations. We show that the KP-II approximation makes correct predictions
about the dynamics of the original scalar FPU system. An existing approximation result is
extended to an arbitrary direction of wave propagation. The main novelty of this work is
the use of Fourier transform in the analysis of the FPU system in strain variables.
Keywords:
Fermi-Pasta-Ulam system; two-dimensional square lattice, lattice dynamics, small-amplitude waves,
Kadometsev-Petviashvili equation, energy estimates.