A compact split step Padé scheme for higher-order nonlinear Schrödinger equation (HNLS) with power law nonlinearity and fourth order dispersion

DOI10.1016/J.CPC.2010.10.016zbMath1217.65177OpenAlexW2070950440MaRDI QIDQ537015

Moussa Smadi, Derradji Bahloul

Publication date: 31 May 2011

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2010.10.016

zbMATH Keywords

stabilitycomparison of methodsnumerical examplesRaman scatteringoptical solitonshigher-order nonlinear Schrödinger equationCrank-Nicolson methodFourier methodpower law nonlinearitycompact Padé schemehigher order dispersionKerr dispersion

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)

Related Items (7)

Jacobi-Gauss-Lobatto collocation method for the numerical solution of \(1+1\) nonlinear Schrödinger equations ⋮ A Chebyshev pseudospectral multidomain method for the soliton solution of coupled nonlinear Schrödinger equations ⋮ A numerical Haar wavelet-finite difference hybrid method for linear and non-linear Schrödinger equation ⋮ On a conservative Fourier spectral Galerkin method for cubic nonlinear Schrödinger equation with fractional Laplacian ⋮ A split-step finite difference method for nonparaxial nonlinear Schrödinger equation at critical dimension ⋮ Finite difference scheme for a higher order nonlinear Schrödinger equation ⋮ A Padé compact high-order finite volume scheme for nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional nonlinear Schrödinger equation
• A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
• The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Padé technique
• Optical solitons in a power law media with fourth order dispersion
• The effect of quintic nonlinearity on the propagation characteristics of dispersion managed optical solitons
• Compact finite difference schemes with spectral-like resolution
• Effect of quintic nonlinearity on soliton collisions in optical fibers
• The solution of coupled Burgers' equations using Adomian-Padé technique
• A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions
• Exact solutions for the fourth order nonlinear Schrödinger equations with cubic and power law nonlinearities
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• Introduction to non-Kerr Law Optical Solitons
• Numerical solution to the unsteady two-dimensional Schrödinger equation using meshless local boundary integral equation method

This page was built for publication: A compact split step Padé scheme for higher-order nonlinear Schrödinger equation (HNLS) with power law nonlinearity and fourth order dispersion