Instability of the finite‐difference split‐step method applied to the generalized nonlinear Schrödinger equation. III. external potential and oscillating pulse solutions
DOI10.1002/num.22071zbMath1367.65120OpenAlexW2398072670WikidataQ115398072 ScholiaQ115398072MaRDI QIDQ5269901
Publication date: 28 June 2017
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/num.22071
numerical examplesnonlinear Schrödinger equationoperator splittingnumerical instabilitysolitonnonlinear evolution equations
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)
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Cites Work
- Nonlinear interaction of solitons and radiation
- Existence and stability of ground states for fully discrete approximations of the nonlinear Schrödinger equation
- A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
- Instability of the finite-difference split-step method applied to the nonlinear Schrödinger equation. I. standing soliton
- Instability of the finite-difference split-step method applied to the nonlinear Schrödinger equation. II. moving soliton
- Instability analysis of the split-step Fourier method on the background of a soliton of the nonlinear Schrödinger equation
- Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
- Variational method: How it can generate false instabilities
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