The Zero Dispersion Limit of the Korteweg-de Vries Equation With Periodic Initial Data

DOI10.2307/2000334zbMath0645.35082OpenAlexW4241210074MaRDI QIDQ3788408

Stephanos Venakides

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000334

zbMATH Keywords

asymptotic behaviourKorteweg-de Vries equationweak limitrepresentation formulaperiodic functionsmall dispersion term

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Inverse problems for PDEs (35R30) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Initial value problems for nonlinear higher-order PDEs (35G25) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Cites Work

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• The spectrum of Hill's equation
• Measure-valued solutions to conservation laws
• Modulational Stability of Two-Phase Sine-Gordon Wavetrains
• The small dispersion limit of the Korteweg-de Vries equation. III
• Modulations of Sinh-Gordon and Sine-Gordon Wavetrains
• Modulations of Perturbed K<scp>d</scp>V Wavetrains
• The zero dispersion limit of the korteweg-de vries equation for initial potentials with non-trivial reflection coefficient
• Long Time Asymptotics of the Korteweg-de Vries Equation
• Asymptotic Behavior of Stability Regions for Hill’s Equation
• The generation of modulated wavetrains in the solution of the Korteweg—de vries equation
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• Convergence of solution to nonlinear dispersive equations
• Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
• The inverse problem for periodic potentials
• Eigenvalues and degeneracies for n-dimensional tensor spherical harmonics

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