Related papers: Small BGK waves and nonlinear Landau damping
We study the nonexistence of multi-dimensional solitary waves for the Euler-Poisson system governing ion dynamics. It is well-known that the one-dimensional Euler-Poisson system has solitary waves that travel faster than the ion-sound…
We study the nonlinear Schr\"odinger equation arising in dipolar Bose-Einstein condensate in the unstable regime. Two cases are studied: the first when the system is free, the second when gradually a trapping potential is added. In both…
In this work, we consider the Vlasov-Poisson-Boltzmann system without angular cutoff and the Vlasov-Poisson-Landau system with Coulomb potential near a global Maxwellian $\mu$. We establish the global existence, uniqueness and large time…
A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions…
In this paper, we investigate the direct and indirect stability of locally coupled wave equations with local viscous damping on cylindrical and non-regular domains without any geometric control condition. If only one equation is damped, we…
Bernstein-Kruskal-Greene (or BGK) modes are ubiquitous nonlinear solutions for the 1D electrostatic Vlasov equation, with the particle distribution function $f$ given as a function of the particle energy. Here, we consider other solutions…
Irregular compactons and peakons from some nonlinear dispersions can be regularized by another type of nonlinear dispersion, defined by a pseudo-differential operator in physical space for the Galerkin truncation preserving finite Fourier…
In this paper, we study the $L^p$-asymptotic stability of the one-dimensional linear damped wave equation with Dirichlet boundary conditions in $[0,1]$, with $p\in (1,\infty)$. The damping term is assumed to be linear and localized to an…
Recent advances in experiment and theory suggest that superfluid $^3$He under planar confinement may form a pair density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a…
This paper is devoted to existence and non-existence results for generalized tran-sition waves solutions of space-time heterogeneous Fisher-KPP equations. When the coefficients of the equation are periodic in space but otherwise depend in a…
In this paper, we study the $L^p$-asymptotic stability with $p\in (1,\infty)$ of the one-dimensional nonlinear damped wave equation with a localized damping and Dirichlet boundary conditions in a bounded domain $(0,1)$. We start by…
We are interested in the stability of a class of totally geodesic wave maps, as recently studied by Abbrescia and Chen, and later by Duan and Ma. The relevant equations of motion are a system of coupled semilinear wave and Klein-Gordon…
The nonlinear theory of Landau damping of electrostatic wave envelopes (WEs) is revisited in a quantum electron-positron (EP) pair plasma. Starting from a Wigner-Moyal equation coupled to the Poisson equation and applying the multiple scale…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
An unstable one-dimensional Bernstein-Greene-Kruskal (BGK) mode has been studied through high-precision numerical simulations. The initial turbulent, periodic equilibrium state is obtained by solving a Vlasov-Poisson system for initially…
This paper sheds new light on the stability properties of solitary wave solutions associated with models of Korteweg-de Vries and Benjamin\&Bona\&Mahoney type, when the dispersion is very lower. Via an approach of compactness, analyticity…
This paper is devoted to the study of the nonlinear stability of the rarefaction waves of the Vlasov-Poisson-Boltzmann system with slab symmetry in the case where the electron background density satisfies an analogue of the Boltzmann…
We assume the macroscopic wave function of a Bose-Einstein condensate as a superposition of Gaussian wave packets, with time-dependent complex width parameters, insert it into the mean-field energy functional corresponding to the…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
In this study, we analyze the behavior of monotone traveling waves of a one-dimensional porous medium equation modeling mechanical properties of living tissues. We are interested in the asymptotics where the pressure, which governs the…