Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse

DOI10.1016/j.physd.2010.03.002zbMath1190.35205OpenAlexW2055824650MaRDI QIDQ979132

Weizhu Bao, Xuanchun Dong, Jack X. Xin

Publication date: 25 June 2010

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2010.03.002

zbMATH Keywords

error boundssine-Gordon equationefficient numerical methodsapproximation beyond critical collapselight bulletsperturbed NLS

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (22)

An efficient and accurate Fourier pseudo-spectral method for the nonlinear Schrödinger equation with wave operator ⋮ A fourth-order difference scheme for the fractional nonlinear Schrödinger equation with wave operator ⋮ Uniformly accurate nested Picard integrators for a system of oscillatory ordinary differential equations ⋮ A linearized energy-conservative finite element method for the nonlinear Schrödinger equation with wave operator ⋮ Hamiltonian-preserving schemes for the two-dimensional fractional nonlinear Schrödinger wave equations ⋮ Mass- and energy-conserving Gauss collocation methods for the nonlinear Schrödinger equation with a wave operator ⋮ Superconvergence analysis of a linearized energy-conservative Galerkin method for the nonlinear Schrödinger equation with wave operator ⋮ Energy conserving local discontinuous Galerkin methods for the nonlinear Schrödinger equation with wave operator ⋮ Uniform Error Bound of an Exponential Wave Integrator for Long-Time Dynamics of the Nonlinear Schrödinger Equation with Wave Operator ⋮ Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator ⋮ A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator ⋮ Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator ⋮ Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime ⋮ Convergence of an energy-conserving scheme for nonlinear space fractional Schrödinger equations with wave operator ⋮ Optimal \(l^\infty\) error estimates of the conservative scheme for two-dimensional Schrödinger equations with wave operator ⋮ Error estimates in the energy space for a Gautschi-type integrator spectral discretization for the coupled nonlinear Klein-Gordon equations ⋮ A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator ⋮ A combination of multiscale time integrator and two-scale formulation for the nonlinear Schrödinger equation with wave operator ⋮ An exponential wave integrator Fourier pseudospectral method for the nonlinear Schrödinger equation with wave operator ⋮ Linear high-order energy-preserving schemes for the nonlinear Schrödinger equation with wave operator using the scalar auxiliary variable approach ⋮ Uniform Error Bounds of an Exponential Wave Integrator for the Long-Time Dynamics of the Nonlinear Klein--Gordon Equation ⋮ Unconditional optimal error estimates and superconvergence analysis of energy-preserving FEM for general nonlinear Schrödinger equation with wave operator

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes
• Numerical solution of the sine-Gordon equation
• Finite-difference solutions of a non-linear Schrödinger equation
• Numerical solution of a nonlinear Klein-Gordon equation
• Comparisons between Maxwell's equations and an extended nonlinear Schrödinger equation
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Evolution of two-dimensional standing and travelling breather solutions for the sine-Gordon equation
• On the numerical solution of the sine-Gordon equation. I: Integrable discretizations and homoclinic manifolds
• Modeling light bullets with the two-dimensional sine-Gordon equation
• A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equation
• Complete integrability of the reduced Maxwell-Bloch equations with permanent dipole
• Global solvability of the Maxwell-Bloch equations from nonlinear optics
• A numerical study of the light bullets interaction in the \((2+1)\) sine-Gordon equation
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• The validity of modulation equations for extended systems with cubic nonlinearities
• An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity
• Spectral Methods in MATLAB
• On the validity of mean-field amplitude equations for counterpropagating wavetrains
• Self-Focusing in the Perturbed and Unperturbed Nonlinear Schrödinger Equation in Critical Dimension
• A singular perturbation problem for an envelope equation in plasma physics
• Pulse evolution for a two-dimensional sine-Gordon equation

This page was built for publication: Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse