The Fourier transform and the discrete Fourier transform, Inverse Problems, vol.5, issue.2, pp.149-164, 1989. ,
DOI : 10.1088/0266-5611/5/2/004
HIGH ORDER EMBEDDED RUNGE-KUTTA SCHEME FOR ADAPTIVE STEP-SIZE CONTROL IN THE INTERACTION PICTURE METHOD, Journal of the Korea Society for Industrial and Applied Mathematics, vol.17, issue.4, pp.238-266, 2013. ,
DOI : 10.12941/jksiam.2013.17.238
URL : https://hal.archives-ouvertes.fr/hal-00874961
Mathematical analysis of adaptive step-size techniques when solving the nonlinear Schr??dinger equation for simulating light-wave propagation in optical fibers, Optics Communications, vol.329, pp.1-9, 2014. ,
DOI : 10.1016/j.optcom.2014.04.081
Embedded Runge???Kutta scheme for step-size control in the interaction picture method, Computer Physics Communications, vol.184, issue.4, pp.1211-1219, 2013. ,
DOI : 10.1016/j.cpc.2012.12.020
URL : https://hal.archives-ouvertes.fr/hal-00797190
Order Estimates in Time of Splitting Methods for the Nonlinear Schr??dinger Equation, SIAM Journal on Numerical Analysis, vol.40, issue.1, pp.26-40, 2002. ,
DOI : 10.1137/S0036142900381497
Numerical methods for ordinary differential equations, 2008. ,
Plane waves numerical stability of some explicit exponential methods for cubic Schrödinger equation, 2013. ,
Exponential time integration of solitary waves of cubic Schr??dinger equation, Applied Numerical Mathematics, vol.91, issue.0, pp.26-45, 2015. ,
DOI : 10.1016/j.apnum.2015.01.001
Vortex dynamics in Bose-Einstein condensate, 2000. ,
Semi-classical Analysis for Nonlinear Schrödinger Equations, World Scientific, 2008. ,
Introduction aux problèmes d'évolution semi-linéaires, 1990. ,
Symmetric Exponential Integrators with an Application to the Cubic Schr??dinger Equation, Foundations of Computational Mathematics, vol.41, issue.2, pp.303-317, 2008. ,
DOI : 10.1007/s10208-007-9016-7
One-stage exponential integrators for nonlinear Schr??dinger equations over long times, BIT Numerical Mathematics, vol.113, issue.2, pp.877-903, 2012. ,
DOI : 10.1007/s10543-012-0385-1
Exponential Time Differencing for Stiff Systems, Journal of Computational Physics, vol.176, issue.2, pp.430-455, 2002. ,
DOI : 10.1006/jcph.2002.6995
Dynamics in Bose-Einstein condensate, 2001. ,
A family of embedded Runge-Kutta formulae, Journal of Computational and Applied Mathematics, vol.6, issue.1, pp.19-26, 1980. ,
DOI : 10.1016/0771-050X(80)90013-3
Exponential Runge???Kutta methods for the Schr??dinger equation, Applied Numerical Mathematics, vol.59, issue.8, pp.1839-1857, 2009. ,
DOI : 10.1016/j.apnum.2009.02.002
Generalized Runge-Kutta Processes for Stiff Initial-value Problems???, IMA Journal of Applied Mathematics, vol.16, issue.1, pp.11-21, 1975. ,
DOI : 10.1093/imamat/16.1.11
How well does the finite Fourier transform approximate the Fourier transform?, Communications on Pure and Applied Mathematics, vol.3, issue.10, pp.1421-1435, 2005. ,
DOI : 10.1002/cpa.20064
Numerical simulation of incoherent optical wave propagation in nonlinear fibers. Eur. Phys, J. -Appl. Phys, vol.64, issue.2, pp.24506-24507, 2013. ,
On the interaction picture, Communications in Mathematical Physics, vol.2, issue.2, pp.120-132, 1966. ,
DOI : 10.1007/BF01645449
Solving ordinary differential equations I: nonstiff problems, 1993. ,
DOI : 10.1007/978-3-662-12607-3
Efficient Adaptive Step Size Method for the Simulation of Supercontinuum Generation in Optical Fibers, Journal of Lightwave Technology, vol.27, issue.18, pp.3984-3991, 2009. ,
DOI : 10.1109/JLT.2009.2021538
Exponential integrators, Acta Numerica, vol.19, pp.209-286, 2010. ,
DOI : 10.1017/S0962492910000048
A Fourth-Order Runge–Kutta in the Interaction Picture Method for Simulating Supercontinuum Generation in Optical Fibers, Journal of Lightwave Technology, vol.25, issue.12, pp.3770-3775, 2007. ,
DOI : 10.1109/JLT.2007.909373
Fourth-Order Time-Stepping for Stiff PDEs, SIAM Journal on Scientific Computing, vol.26, issue.4, pp.1214-1233, 2005. ,
DOI : 10.1137/S1064827502410633
Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants, SIAM Journal on Numerical Analysis, vol.4, issue.3, pp.372-380, 1967. ,
DOI : 10.1137/0704033
On splitting methods for Schr??dinger-Poisson and cubic nonlinear Schr??dinger equations, Mathematics of Computation, vol.77, issue.264, pp.2141-2153, 2008. ,
DOI : 10.1090/S0025-5718-08-02101-7
A split-step Fourier method for the complex modified Korteweg-de Vries equation, Computers & Mathematics with Applications, vol.45, issue.1-3, pp.503-514, 2003. ,
DOI : 10.1016/S0898-1221(03)80033-0
Optimization of the split-step fourier method in modeling optical-fiber communications systems, Journal of Lightwave Technology, vol.21, issue.1, p.61, 2003. ,
DOI : 10.1109/JLT.2003.808628
Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schr??dinger Equations, SIAM Journal on Numerical Analysis, vol.50, issue.6, pp.3231-3258, 2012. ,
DOI : 10.1137/120866373
A modern approach to quantum mechanics. International series in pure and applied physics, 2000. ,
Split-Step Methods for the Solution of the Nonlinear Schr??dinger Equation, SIAM Journal on Numerical Analysis, vol.23, issue.3, pp.485-507, 1986. ,
DOI : 10.1137/0723033