Muslu, G. and Erbay, H. (2005) Higher-Order Split-Step Fourier Schemes for the Generalized Nonlinear Schrödinger Equation. Mathematics and Computers in Simulation, 67, 581-595. https://doi.org/10.1016/j.matcom.2004.08.002

has been cited by the following article:

• TITLE: Fourier Pseudospectral Solution for a 2D Nonlinear Paraxial Envelope Equation of Laser Interactions in Plasmas

  AUTHORS: Abdelrahman I. Mahdy

  KEYWORDS: Laser Plasmas Interactions, Laser Envelope-Equation, Fourier Pseudospectral Method, Nonlinear Schrödinger Equation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.12, December 20, 2016

  ABSTRACT: We apply a Fourier pseudospectral algorithm to solve a 2D nonlinear paraxial envelope-equation of laser interactions in plasmas. In this algorithm, we first use the second order Strang time-splitting method to split the envelope-equation into a number of equations, next we spatially discrete the filed quantity and its spatial derivatives in these equations in term of Fourier interpolation polynomials (FFT), finally we sequentially integrate the resultant equations by means of a discrete integration method in order to obtain the solution of the envelope-equation. We carry out several numerical tests to illustrate the efficiency and to determine accuracy of the algorithm. In addition, we conduct a number of numerical experiments to examine its performance. The numerical results have shown that the algorithm is highly efficient and sufficiently accurate to solve the 2D envelope-equation, furthermore, it yields an optimal performance in simulating fundamental phenomena in laser interactions in plasmas.