WIAS Preprint No. 3070, (2023)
Stability of the higher-order splitting methods for the generalized nonlinear Schrödinger equation
Authors
- Amiranashvili, Shalva
ORCID: 0000-0002-8132-882X - Čiegis, Raimondas
2020 Mathematics Subject Classification
- 78A40 78A60 91G60
Keywords
- Nonlinear optics, nonlinear fibers, nonlinear Schrödinger equation, generalized nonlinear Schrödinger equation, modulation instability, four-wave mixing, spurious instabilities, splitting methods
DOI
Abstract
The numerical solution of the generalized nonlinear Schrödinger equation by explicit splitting methods can be disturbed by so-called spurious instabilities. They are manifested by the appearance of extraneous spectral peaks which change their position in the frequency domain and disappear with decreasing integration step. The spurious instabilities can coexist with the true physical ones, like modulation instability, in which case they are particularly difficult to detect. We consider an arbitrary multiplicative splitting method and discuss conditions necessary for the absence of spurious instabilities.
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