Numerical solutions of the Korteweg-de Vries equation using the periodic scattering transform \(\mu\)-representation

DOI10.1016/0167-2789(90)90163-JzbMath0707.65089OpenAlexW2021922555MaRDI QIDQ919771

Enrico Segre, Alfred R. Osborne

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0167-2789(90)90163-j

zbMATH Keywords

periodic boundary conditionstrace formulaKorteweg-de Vries equationvariable step sizewave amplitudehypoelliptic functionsmu-representationperiodic scattering transformsecond order Taylor series expansion

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Numerical methods for initial value problems involving ordinary differential equations (65L05) Applications to the sciences (65Z05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (9)

Automatic algorithm for the numerical inverse scattering transform of the Korteweg-de Vries equation ⋮ Comparative analysis of bore propagation over long distances using conventional linear and KdV-based nonlinear Fourier transform ⋮ Numerical finite-gap integration of the Zabusky–Kruskal problem ⋮ Hidden solitons in the Zabusky-Kruskal experiment: analysis using the periodic, inverse scattering transform ⋮ Computation of the direct scattering transform for the nonlinear Schrödinger equation ⋮ Identifying coherent structures in nonlinear wave propagation ⋮ Internal solitary waves in the ocean: analysis using the periodic, inverse scattering transform ⋮ Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis ⋮ The inverse scattering transform: tools for the nonlinear Fourier analysis and filtering of ocean surface waves.

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