相关论文: Exponential stability for the nonlinear Schr\"odin…
In this paper, we study the defocusing nonlinear Schr\"{o}dinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using…
In this paper we consider the Schr\"odinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schr\"odinger equation with…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…
Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schr\"odinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context…
We present general results on exponential decay of finite energy solutions to stationary nonlinear Schr\"odinger equations.
We prove asymptotic stability of trapped solitons in the generalized nonlinear Schr\"odinger equation with a potential in dimension 1 and for even potential and even initial conditions.
We continue our series devoted, after references \cite{CM24D1} and \cite{CM243}, at proving the asymptotic stability of ground states of the pure power Nonlinear Schr\"odinger equation on the line. Here we assume some results on the…
We consider a dispersive equation of Schr{\"o}dinger type with a non-linearity slightly larger than cubic by a logarithmic factor. This equation is supposed to be an effective model for stable two dimensional quantum droplets with LHY…
We construct stationary statistical solutions of a deterministic unforced nonlinear Schr\"odinger equation, by perturbing it by a linear damping $\gamma u$ and a stochastic force whose intensity is proportional to $\sqrt \gamma$, and then…
We prove that solutions to non-linear Schr\"odinger equations in two dimensions and in the exterior of a bounded and smooth star-shaped obstacle scatter in the energy space. The non-linear potential is defocusing and grows at least as the…
The aim of this work is to demonstrate the effectiveness of the extension theory of symmetric operators in the investigation of the stability of standing waves for the nonlinear Schr\"odinger equations with two types of non-linearities…
This article addresses the stabilizability of a perturbed quintic defocusing Schr\"odinger equation in $\mathbb{R}^{3}$ at the $H^1$--energy level, considering the influence of a damping mechanism. More specifically, we establish a profile…
We transpose work by K.Yajima and by T.Mizumachi to prove dispersive and smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\"odinger equation (NLS) in 2D. As an application we extend to…
We consider a Nonlinear Schr\"odinger Equation with a very general non linear term and with a trapping $\delta $ potential on the line. We then discuss the asymptotic behavior of all its small solutions, generalizing a recent result by…
We consider the damped nonlinear Schr\''{o}dinger equation with saturation: i.e., the complex evolution equation contains in its left hand side, besides the potential term $V(x)u,$ a nonlinear term of the form $\mathrm{i}\mu…
In this paper we investigate the uniform exponential stability of the system $\frac{dx(t)}{dt}=Ax(t)-\rho Bx(t), \; (\rho >0), $ where the unbounded operator $A$ is the infinitesimal generator of a linear $C_0-$semigroup of contractions…
In this paper, a nonlinear Schr\"odinger equation with an attractive (focusing) delta potential and a repulsive (defocusing) double power nonlinearity in one spatial dimension is considered. It is shown, via explicit construction, that both…
We study the stability of a type of stratified flows of the two dimensional inviscid incompressible MHD equations with velocity damping. The exponential stability for the perturbation near certain stratified flow is investigated in a…
We consider the nonlinear Schr\"odinger equation on a unit ball in one and two dimensions with Dirichlet boundary conditions, which have stabilizing effect on solutions behavior. In particular, we confirm that the ground state solutions are…
We study the complex Ginzburg-Landau equation posed on possibly unbounded domains, including some singular and saturated nonlinear damping terms. This model interpolates between the nonlinear Schr{\"o}dinger equation and dissipative…