Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation
From MaRDI portal
Publication:1765709
DOI10.1016/j.matcom.2004.08.002zbMath1064.65117OpenAlexW2085725825MaRDI QIDQ1765709
Publication date: 23 February 2005
Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matcom.2004.08.002
numerical experimentFourier methodSolitary wavesSplit-step methodGeneralized nonlinear Schrödinger equation
NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)
Related Items
Exponential time differencing Crank-Nicolson method with a quartic spline approximation for nonlinear Schrödinger equations ⋮ Additive splitting methods for parallel solutions of evolution problems ⋮ Numerical study of fourth-order linearized compact schemes for generalized NLS equations ⋮ Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations ⋮ Freak wave statistics on collinear currents ⋮ A time-splitting pseudospectral method for the solution of the Gross-Pitaevskii equations using spherical harmonics with generalised-Laguerre basis functions ⋮ A numerical study of the long wave--short wave interaction equations ⋮ Optimizing initial chirp for efficient femtosecond wavelength conversion in silicon waveguide by split-step Fourier method ⋮ Numerical methods for a class of generalized nonlinear Schrödinger equations ⋮ Numerical study of the model described by the fourth order generalized nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinearity ⋮ Time–space Jacobi pseudospectral simulation of multidimensional Schrödinger equation ⋮ Accelerating the Fourier split operator method via graphics processing units ⋮ Quintic B-spline collocation method for the generalized nonlinear Schrödinger equation ⋮ Modeling the long-range wave propagation by a split-step wavelet method ⋮ A linearly semi-implicit compact scheme for the Burgers–Huxley equation ⋮ Numerical simulation of blow-up solutions for the generalized Davey–Stewartson system ⋮ Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method ⋮ Efficiency of exponential time differencing schemes for nonlinear Schrödinger equations ⋮ WKB analysis for the three coupled long wave–short wave interaction equations ⋮ Spectral solutions to the Korteweg-de-Vries and nonlinear schrodinger equations ⋮ Description of dispersive wave emission and supercontinuum generation in silicon waveguides using split-step Fourier and Runge-Kutta integration methods ⋮ A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schrödinger equation ⋮ Higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations ⋮ Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method ⋮ Numerical studies on Boussinesq-type equations via a split-step Fourier method ⋮ Symplectic and multi-symplectic methods for coupled nonlinear Schrödinger equations with periodic solutions ⋮ An open source virtual laboratory for the Schrödinger equation ⋮ Numerical solution of the 3D time dependent Schrödinger equation in spherical coordinates: Spectral basis and effects of split-operator technique ⋮ Analytical and numerical methods for the CMKdV-II equation ⋮ A real space split operator method for the Klein-Gordon equation ⋮ The coupled nonlinear Schrödinger equations describing power and phase for modeling phase-sensitive parametric amplification in silicon waveguides ⋮ Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations
Cites Work
- Unnamed Item
- Unnamed Item
- Pseudo-spectral solution of nonlinear Schrödinger equations
- Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
- Spectral methods and mappings for evolution equations on the infinite line
- A numerical study of the nonlinear Schrödinger equation involving quintic terms
- Difference schemes for solving the generalized nonlinear Schrödinger equation
- The rate of convergence of Fourier coefficients for entire functions of infinite order with application to the Weideman-Cloot Sinh-mapping for pseudospectral computations on an infinite interval
- Symplectic integration of Hamiltonian wave equations
- The solution of nonlinear Schrödinger equations using orthogonal spline collocation
- A split-step Fourier method for the complex modified Korteweg-de Vries equation.
- A fast spectral algorithm for nonlinear wave equations with linear dispersion
- Splitting methods
- Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
- Solving the generalized nonlinear Schrödinger equation via quartic spline approximation