Geodesic
The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics
Balac, Stéphane1  ; Fernandez, Arnaud1  ; Mahé, Fabrice2 ; Méhats, Florian2  ; Texier-Picard, Rozenn3 
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 945-964

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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.

DOI : 10.1051/m2an/2015060
Classification : 65M12, 65M15, 65L06, 65T50, 78A60
Keywords: Interaction picture method, symmetric Split-Step method, Runge−Kutta method, nonlinear optics, nonlinear Schrödinger equation

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

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. 
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     author = {Balac, St\'ephane and Fernandez, Arnaud and Mah\'e, Fabrice and M\'ehats, Florian and Texier-Picard, Rozenn},
     title = {The {Interaction} {Picture} method for solving the generalized nonlinear {Schr\"odinger} equation in optics},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {945--964},
     publisher = {EDP-Sciences},
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Balac, Stéphane; Fernandez, Arnaud; Mahé, Fabrice; Méhats, Florian; Texier-Picard, Rozenn. The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 945-964. doi: 10.1051/m2an/2015060

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