The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics∗
1 FOTON, Université de Rennes I, CNRS, UEB, Enssat, 6 rue de Kerampont, 22305 Lannion, France.
2 IRMAR, Université de Rennes I, CNRS, UEB, Campus de Beaulieu, 35042 Rennes, France.
3 IRMAR, ENS Rennes, CNRS, UEB, av. R. Schuman, 35170 Bruz, France.
Received: 18 November 2014
Revised: 3 April 2015
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 used 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.
Mathematics Subject Classification: 65M12 / 65M15 / 65L06 / 65T50 / 78A60
Key words: Interaction picture method / symmetric Split-Step method / Runge−Kutta method / nonlinear optics / nonlinear Schrödinger equation
© EDP Sciences, SMAI 2016