APPROXIMATED EXPONENTIAL INTEGRATORS FOR THE STOCHASTIC MANAKOV EQUATION
Journal article, 2023

. This article presents and analyzes an approximated exponential integrator for the (inhomogeneous) stochastic Manakov system. This system of SPDE occurs in the study of pulse propagation in randomly birefringent optical fibers. For a globally Lipschitz-continuous nonlinearity, we prove that the strong order of the time integrator is 1/2. This is then used to prove that the approximated exponential integrator has convergence order 1/2 in probability and almost sure order 1/2-, in the case of the cubic nonlinear coupling which is relevant in optical fibers. Finally, we present several numerical experiments in order to support our theoretical findings and to illustrate the efficiency of the approximated exponential integrator as well as a modified version of it.

Coupled system of nonlinear Schr?dinger equations

Exponential integrators

Numerical schemes

Stochastic partial differential equations

Convergence rates

Convergence in probability

Almost sure convergence

Strong convergence

Stochastic Manakov equation

Author

Andre Berg

Umeå University

David Cohen

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Guillaume Dujardin

University of Lille

Journal of Computational Dynamics

2158-2505 (eISSN)

Vol. 10 2 323-344

Numerical analysis and simulation of PDEs with random dispersion

Swedish Research Council (VR) (2018-04443), 2019-01-01 -- 2022-12-31.

Subject Categories

Computational Mathematics

Other Physics Topics

Control Engineering

Mathematical Analysis

DOI

10.3934/jcd.2023002

More information

Latest update

7/3/2024 1