In this paper, we consider the following nonlinear Schrödinger equation: iut+ Δ gu+ ia (x) u−|
u| p− 1 u= 0 (x, t)∈ M×(0,+∞), u (x, 0)= u 0 (x) x∈ M,(0.1) where (𝓜, g) is a smooth complete …

{\bf Abstract}\,\, We consider the following nonlinear Schr\"{o} dinger equation on exterior
domain.\begin {equation}\begin {cases} iu_t+\Delta_g u+ ia (x) u-| u|^{p-1} u= 0\qquad (x …

In this paper, we study the defocusing nonlinear Schrödinger equation with a locally
distributed damping on a smooth bounded domain as well as on the whole space and on an …

We study in this paper the well-posedness and stability for two linear Schrödinger equations
in d-dimensional open bounded domain under Dirichlet boundary conditions with an infinite …

We are concerned with the existence as well as the exponential stability in H 1-level for the
damped defocusing Schrödinger equation posed in a two-dimensional exterior domain Ω …

We derive an exponential decay rate of energy for the cubic Schrödinger equation on a
dissipative waveguide with a damping term that is effective locally on a neighborhood at the …

In this article, we prove the (uniform) global exponential stabilization of the cubic defocusing
Schr\" odinger equation on the torus d-dimensional torus, for d= 1, 2 or 3, with a linear …

In this work, we study the existence at the L2–level as well as the stability for the high order
nonlinear Schrödinger equation in a bounded interval with a localized damping term. To …