Numerical algorithms for the direct spectral transform with applications to nonlinear Schrödinger type systems

DOI10.1006/jcph.1998.6087zbMath0924.65076OpenAlexW2096695668MaRDI QIDQ1287235

K. Appert

Publication date: 2 May 1999

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/9f0d5ca40a15f3cdd6adfc4a664ec39102a0af36

zbMATH Keywords

algorithmsconvergenceeigenvaluenonlinear Schrödinger equationRunge-Kutta methodZakharov-Shabat spectral problemwave functionsoptical fiber

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items

Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system associated with nonlinear Schrödinger equation ⋮ Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem ⋮ Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation

Cites Work

• Computation of the direct scattering transform for the nonlinear Schrödinger equation
• A quasi-periodic route to chaos in a near-integrable PDE
• The inverse scattering transform: Semi-infinite interval
• Guiding-center soliton
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