The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics

Stéphane Balac (1) , Arnaud Fernandez (1) , Fabrice Mahé (2) , Florian Méhats (3, 2) , Rozenn Texier-Picard (2)

1 FOTON - Fonctions Optiques pour les Technologies de l'informatiON
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 IPSO - Invariant Preserving SOlvers

The ''interaction picture'' (IP) method is a very promising alternative to Split-Step methods for solving certain type of partial differential equations such as the nonlinear Schrödinger equation involved in the simulation of wave propagation in optical fibers. The method exhibits interesting convergence properties and is likely to provide more accurate numerical results than cost comparable Split-Step methods such as the Symmetric Split-Step method. In this work we investigate in detail the numerical properties of the IP method and carry out a precise comparison between the IP method and the Symmetric Split-Step method.

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Balac, Arnaud Fernandez, Fabrice Mahé, Florian Méhats, Rozenn Texier-Picard. The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics. 2014. ⟨hal-00850518v2⟩