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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shalva Amiranashvili & Uwe Bandelow & Raimondas Čiegis, 2025. "Stability of the Additive Splitting Methods for the Generalized Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 13(8), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1301-:d:1635611
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