Numerical methods for a class of generalized nonlinear Schrödinger equations

DOI10.3934/krm.2015.8.215zbMath1327.65156OpenAlexW2315878670MaRDI QIDQ888723

Shalva Amiranashvili, Raimondas Čiegis, Mindaugas Radziunas

Publication date: 2 November 2015

Published in: Kinetic and Related Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/krm.2015.8.215

zbMATH Keywords

stabilizationspectral methodnumerical experimentsplitting methodfinite diiference methodgeneralized nonlinear Schrödinger equations

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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Cites Work

• Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
• Pseudo-spectral solution of nonlinear Schrödinger equations
• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• High-order time-splitting Hermite and Fourier spectral methods
• On the convergence of splitting methods for linear evolutionary Schrödinger equations involving an unbounded potential
• Solution of the Schrödinger equation by a spectral method
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• Regular and chaotic dynamics.
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation
• Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
• Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation
• EFFECTIVE NUMERICAL INTEGRATION OF TRAVELING WAVE MODEL FOR EDGE‐EMITTING BROAD‐AREA SEMICONDUCTOR LASERS AND AMPLIFIERS
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• Numerical Algorithms for Schrödinger Equation with Artificial Boundary Conditions
• Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
• On a class of conservative, highly accurate Galerkin methods for the Schrödinger equation
• Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
• On the Construction and Comparison of Difference Schemes
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