Related papers: On dispersion managed nonlinear Schr\"odinger equa…
This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schr\"odinger equation. In this part we study the diffraction managed discrete…
In this paper, the trial function method is employed to find the exact solutions for high-order nonlinear Schr\"odinger equations with time-dependent coefficients. This system describes the propagation of ultrashort light pulses in…
The method for computation of conditional probability density function for the nonlinear Schr\"odinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of…
We analyze dynamical properties of the logarithmic Schr{\"o}dinger equation under a quadratic potential. The sign of the nonlinearity is such that it is known that in the absence of external potential, every solution is dispersive, with a…
We consider a quasilinear Schr\"odinger equation on $\mathbb R$ for which the dispersive effects degenerate when the solution vanishes. We first prove local well-posedness for sufficiently smooth, spatially localized, degenerate initial…
We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…
We consider the nonlinear Schr\"odinger equation with focusing power-type nonlinearity on compact graphs with at least one terminal edge, i.e. an edge ending with a vertex of degree 1. On the one hand, we introduce the associated action…
We consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of ring-profiled optical vortex solitons appearing…
The interface problem for the linear Schr\"odinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the…
Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr\"odinger equation, which describes the evolution of the signal in the link, numerically.…
In this paper, we study a Schr\"odinger-type equation featuring a derivative in the nonlinear term and incorporating diffusion effects. This type of equation arises in various physical applications, such as modeling low-order magnetization…
This paper is devoted to the averaged controllability of the random Schr\"odinger equation, with diffusivity as a random variable drawn from a general probability distribution. First, we show that the solutions to these random Schr\"odinger…
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies…
We consider the Schrodinger equation with a logarithmic nonlinearity and a repulsive harmonic potential. Depending on the parameters of the equation, the solution may or may not be dispersive. When dispersion occurs, it does with an…
The capacity of the channel defined by the stochastic nonlinear Schr\"odinger equation, which includes the effects of the Kerr nonlinearity and amplified spontaneous emission noise, is considered in the case of zero dispersion. In the…
The nonlinear wave and Schrodinger equations on Euclidean space of any dimension, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space of index s whenever the…
We prove global well-posedness for the cubic nonlinear Schr\"odinger equation for periodic initial data in the mass-critical dimension $d=2$ for initial data of arbitrary size in the defocusing case and data below the ground state threshold…
We consider the nonlinear Schrodinger equation with a modified spatial dispersion, given either by an homogeneous Fourier multiplier, or by a bounded Fourier multiplier. Arguments based on ordinary differential equations yield ill-posedness…
We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.
We establish the global well-posedness of the derivative nonlinear Schr\"odinger equation with periodic boundary condition in the Sobolev space $H^{\frac12}$, provided that the mass of initial data is less than $4\pi$. This result matches…