Title :

Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System

Author(s) :

Berg, André [Auteur]
Umeå University = Umeå Universitet
Cohen, David [Auteur]
Department of Mathematical Sciences [Chalmers]
Dujardin, Guillaume [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]

Journal title :

Journal of Scientific Computing

Publisher :

Springer Verlag

Publication date :

2021-05-22

ISSN :

0885-7474

English keyword(s) :

Stochastic partial differential equations
Stochastic Manakov equation
Coupled system of stochastic nonlinear Schrödinger equations
Numerical schemes
Splitting scheme
Lie–Trotter scheme
Strong convergence
Convergence in probability
Almost sure convergence
Convergence rates
Blowup

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Science non linéaire [physics]/Formation de Structures et Solitons [nlin.PS]
Physique [physics]/Physique [physics]/Optique [physics.optics]

English abstract : [en]

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 birefringent optical fibers. First, we prove ...
Show more >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 birefringent optical fibers. First, we prove that the strong order of the numerical approximation is 1/2 if the nonlinear term in the system is globally Lipschitz. Then, we show that the splitting scheme has convergence order 1/2 in probability and almost sure order 1/2- in the case of a cubic nonlinearity. We provide several numerical experiments illustrating the aforementioned results and the efficiency of the Lie-Trotter splitting scheme. Finally, we numerically investigate the possible blowup of solutions for some power-law nonlinearities.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL