Computation of the direct scattering transform for the nonlinear Schrödinger equation

DOI10.1016/0021-9991(92)90370-EzbMath0761.65093OpenAlexW2073185643MaRDI QIDQ1201704

G. Boffetta, Alfred R. Osborne

Publication date: 17 January 1993

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

Full work available at URL: https://doi.org/10.1016/0021-9991(92)90370-e

zbMATH Keywords

nonlinear Schrödinger equationKorteweg-de Vries equationspectral methodsine-Gordon equationnonlinear wave equationsnumerical algorithmsinh-Gordon equationsdirect scattering transformnarrow-banded wave trainnonlinear Fourier spectrum

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Applications to the sciences (65Z05)

Related Items (14)

Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system associated with nonlinear Schrödinger equation ⋮ Reliable computation of the eigenvalues of the discrete KdV spectrum ⋮ Oscillations of the soliton parameters in nonlinear interference phenomena ⋮ Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation ⋮ Numerical inverse scattering for the Korteweg-de Vries and modified Korteweg-de Vries equations ⋮ Variationally obtained approximate eigenvalues of the Zakharov-Shabat scattering problem for real potentials. ⋮ Structural transformation of eigenvalues for a perturbed algebraic soliton potential. ⋮ Finite difference methods for an AKNS eigenproblem ⋮ Adiabatic and non-adiabatic soliton interactions in nonlinear optics ⋮ An accurate \(\mathcal{O}(N^2)\) floating point algorithm for the Crum transform of the KdV equation ⋮ Incorporating Radiation in Noise-Induced Phase Evolution of Optical Solitons ⋮ Numerical analysis of the Hirota equation: Modulational instability, breathers, rogue waves, and interactions ⋮ Numerical algorithms for the direct spectral transform with applications to nonlinear Schrödinger type systems ⋮ Prediction of the number of solitons for initial value of nonlinear Schrödinger equation based on the deep learning method

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