One-dimensional chains are used as a fundamental model of condensed matter, and have
constituted the starting point for key developments in nonlinear physics and complex …

We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear
Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that …

In a series of previous works (arxiv: 2104.11204, arxiv: 2110.04565, arxiv: 2301.07063), we
gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small …

Our goal in this paper is to initiate the rigorous investigation of wave turbulence and
derivation of wave kinetic equations (WKEs) for water waves models. This problem has …

This paper completes the program started in arxiv: 2104.11204 and arxiv: 2110.04565
aiming at providing a full rigorous justification of the wave kinetic theory for the nonlinear …

Starting from a stochastic Zakharov-Kuznetsov (ZK) equation on a lattice, the previous work
[ST21] by the last two authors gave a derivation of the homogeneous 3-wave kinetic …

We consider the kinetic wave equation arising in wave turbulence to describe the Fourier
spectrum of solutions to the cubic Schrödinger equation. This equation has two Kolmogorov …

We introduce a simplified model for wave turbulence theory—the Wick nonlinear
Schrödinger equation, of which the main feature is the absence of all self‐interactions in the …

We provide a rigorous derivation of Boltzmann's kinetic equation from the hard-sphere
system for rarefied gas, which is valid for arbitrarily long time as long as the solution to the …

In this work, we study the random series expansion of a multidimensional KdV type equation
with a diffusion term, the so-called Zakharov-Kuznetsov (ZK) equation. We impose random …