Split-step methods for the solution of the nonlinear Schro¨dinger equation
SIAM Journal on Numerical Analysis
A numerical study of the nonlinear Schro¨dinger equation involving quintic terms
Journal of Computational Physics
Pseudo-spectral solution of nonlinear Schro¨dinger equations
Journal of Computational Physics
Spectral methods and mappings for evolution equations on the infinite line
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Difference schemes for solving the generalized nonlinear Schrödinger equation
Journal of Computational Physics
A fast spectral algorithm for nonlinear wave equations with linear dispersion
Journal of Computational Physics
Solving the Generalized Nonlinear Schrödinger Equation via Quartic Spline Approximation
Journal of Computational Physics
A numerical study of the long wave-short wave interaction equations
Mathematics and Computers in Simulation
A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schrödinger equation
Journal of Computational Physics
Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
A real space split operator method for the Klein-Gordon equation
Journal of Computational Physics
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The generalized nonlinear Schrodinger (GNLS) equation is solved numerically by a split-step Fourier method. The first, second and fourth-order versions of the method are presented. A classical problem concerning the motion of a single solitary wave is used to compare the first, second and fourth-order schemes in terms of the accuracy and the computational cost. This numerical experiment shows that the split-step Fourier method provides highly accurate solutions for the GNLS equation and that the fourth-order scheme is computationally more efficient than the first-order and second-order schemes. Furthermore, two test problems concerning the interaction of two solitary waves and an exact solution that blows up in finite time, respectively, are investigated by using the fourth-order split-step scheme and particular attention is paid to the conserved quantities as an indicator of the accuracy. The question how the present numerical results are related to those obtained in the literature is discussed.