Related papers: Comment on "The Stochastic Nonlinear Schr\"odinger…
The system discussed recently in L. Cao and D. J. Wu, Europhys. Lett. {\bf 61}, (2003) 593 merely reproduces properties of the input signal.
We consider the stochastic nonlinear Schr\"odinger equation driven by linear multiplicative noise in the mass-supercritical case. Given arbitrary $K$ solitary waves with distinct speeds, we construct stochastic multi-solitons pathwisely in…
We address the Cauchy problem for a nonlinear Schr{\"o}dinger equation where the dispersion is modulated by a deterministic noise. The noise is understood as the derivative of a self-affine function of order H $\in$ (0, 1). Due to the…
We study the periodic non-linear Schrodinger equations with odd integer power nonlinearities, for initial data which are assumed to be small in some negative order Sobolev space, but which may have large L^2 mass. These equations are known…
The Nonlinear Schroedinger Equation (NLSE) with a random potential is motivated by experiments in optics and in atom optics and is a paradigm for the competition between the randomness and nonlinearity. The analysis of the NLSE with a…
We develop resonance-based low-regularity numerical integrators for stochastic Schr"odinger equations with additive $Q$-Wiener noise, covering both the linear equation with rough potential and the cubic nonlinear case. For the linear…
We prove pathwise uniqueness for solutions of the nonlinear Schr\"{o}dinger equation with conservative multiplicative noise on compact 3D manifolds. In particular, we generalize the result by Burq, G\'erard and Tzvetkov (N. Burq, P.…
We prove global well-posedness for the cubic nonlinear Schr\"odinger equation with nonlinearity concentrated on a homogeneous Poisson process.
Here is investigated the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schr\"odinger equation perturbed by a linear multiplicative Wiener process. The existence of…
We give decay estimates of the solution to the linear Schr\"odinger equation in dimension $d \geq 3$ with a small noise which is white in time and colored in space. As a consequence, we also obtain certain asymptotic behaviour of the…
In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from…
The study is devoted to the interpretation and wellposedness of the stochastic NLS model \begin{equation*} (\imath \partial_t-\Delta)u=|u|^2+\dot{B}, \quad u_0=0,\quad \quad t\in \mathbb{R}, \ x\in \mathbb{T}, \end{equation*} where…
We study the nonlinear Schr\"odinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. On the lattice we prove that solutions are polynomially…
In this short note, we present a construction for the log-log blow up solutions to focusing mass-critical stochastic nonlinear Schr\"oidnger equations with multiplicative noises. The solution is understood in the sense of controlled rough…
In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic nonlinear Schr\"{o}dinger equation, with either focusing or defocusing nonlinearity, driven by nonlinear multiplicative L\'evy noise in the Marcus…
This paper is concerned with the existence and uniqueness of the solution for the stochastic fast logarithmic equation with Stratonovich multiplicative noise in $\mathbb{R}^{d}$ for $d\geqslant 3$. It provides an answer to a critical case…
We consider the linear and non linear cubic Schr\"odinger equations with periodic boundary conditions, and their approximations by splitting methods. We prove that for a dense set of arbitrary small time steps, there exists numerical…
In this article, we study a $d$-dimensional stochastic quadratic nonlinear Schr\"{o}dinger equation (SNLS), driven by a fractional derivative (of order $-\alpha<0$) of a space-time white noise: $$\left\{ \begin{array}{l}i\partial_t u-\Delta…
We consider a derivative nonlinear Schr\"odinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability/instability results that depend on the strength of the…
New Strichartz estimates for the modulated cubic nonlinear Schr\"{o}dinger equation are proved. These Strichartz estimates allow us to show that this equation is pathwise locally well-posed. We also show that improved Strichartz estimates…