Stability of the Additive Splitting Methods for the Generalized Nonlinear Schrödinger Equation

Shalva Amiranashvili, Uwe Bandelow and Raimondas Čiegis ()
Additional contact information
Shalva Amiranashvili: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany
Uwe Bandelow: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany
Raimondas Čiegis: Department of Mathematical Modelling, Vilnius Gediminas Technical University, Sauletekio Av. 11, 10223 Vilnius, Lithuania

Mathematics, 2025, vol. 13, issue 8, 1-19

Abstract: Splitting methods provide an efficient approach to solving evolutionary wave equations, especially in situations where dispersive and nonlinear effects on wave propagation can be separated, as in the generalized nonlinear Schrödinger equation (GNLSE). However, such methods are explicit and can lead to numerical instabilities. We study these instabilities in the context of the GNLSE. Results previously obtained for multiplicative splitting methods are extended to additive splittings. An estimate of the largest possible integration step is derived and tested. The results are important when many solutions of GNLSE are needed, e.g., in optimization problems or statistical calculations.

Keywords: nonlinear fibers; nonlinear Schrödinger equation; generalized nonlinear Schrödinger equation; modulation instability; numerical instabilities; splitting methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/8/1301/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/8/1301/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:8:p:1301-:d:1635611

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().