This paper studies the behavior of solitons in the Korteweg–de Vries equation under the
influence of multiplicative noise. We introduce stochastic processes that track the amplitude …

We prove that the solutions to the discrete nonlinear Schrödinger equation with non-local
algebraically decaying coupling converge strongly in L 2 (R 2) to those of the continuum …

We study waves on infinite one-dimensional lattices of particles that each interact with all
others through power-law forces. The inverse-cube case corresponds to Calogero–Moser …

The “classical” thermodynamic and statistical mechanical theories of Gibbs and Boltzmann
are both predicated on axiomatic assumptions whose applicability is hard to ascertain …

In this study, we consider the nonlinear Schödinger equation (NLS) with the zero-boundary
condition on a two-or three-dimensional large finite cubic lattice. We prove that its solution …

The Korteweg-de Vries (KdV) equation is known as a universal equation describing various
long waves in dispersive systems. In this article, we prove that in a certain scaling regime, a …

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 …

It is well known that the Korteweg-de Vries (KdV) equation and its generalizations serve as
modulation equations for traveling wave solutions to generic Fermi-Pasta-Ulam-Tsingou …

We prove that the solutions to the discrete nonlinear Schrödinger equation with non-local
algebraically decaying coupling converge strongly in L2 (R2) to those of the continuum …

Abstract The Fermi-Pasta-Ulam-Tsingou (FPUT) lattice became of great mathematical
interest when it was observed that it exhibited a near-recurrence of its initial condition …