This paper is concerned with the numerical integration in time of nonlinear Schrödinger
equations using different methods preserving the energy or a discrete analogue of it. The …

The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein
scheme) are known to diverge strongly and numerically weakly in the case of one …

Resonance based numerical schemes are those in which cancellations in the oscillatory
components of the equation are taken advantage of in order to reduce the regularity …

The Manakov model, a framework of coupled non-linear Schrödinger equations, reflects an
essential integrable model in non-linear physics, particularly used to analyze soliton …

This article is devoted to the numerical study of a nonlinear Schrödinger equation in which
the coefficient in front of the group velocity dispersion is multiplied by a real valued Gaussian …

This article deals with the numerical integration in time of the nonlinear Schrödinger
equation with power law nonlinearity and random dispersion. We introduce a new explicit …

This article analyses the convergence of the Lie–Trotter splitting scheme for the stochastic
Manakov equation, a system arising in the study of pulse propagation in randomly …

This article presents and analyzes an approximated exponential integrator for the
(inhomogeneous) stochastic Manakov system. This system of SPDE occurs in the study of …

This article presents and analyses an exponential integrator for the stochastic Manakov
equation, a system arising in the study of pulse propagation in randomly birefringent optical …

The Gross-Pitaevskii equation with white noise in time perturbations of the harmonic
potential is considered. In this article we define a Crank-Nicolson scheme based on a …