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Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System
Abstract
International audienceThis 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- info:eu-repo/semantics/article
- Journal articles
- 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
- 65C30, 65C50, 65J08, 60H15, 60M15, 60-08, 35Q55
- [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
- [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
- [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS]
- [PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics]