The Whitham-type equations and linear overdetermined systems of Euler- Poisson-Darboux type

DOI10.1215/S0012-7094-94-07410-3zbMath0826.35092OpenAlexW1551875252MaRDI QIDQ1331695

Fei-Ran Tian

Publication date: 25 August 1994

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-94-07410-3

zbMATH Keywords

Krichever's algebraic- geometric schemeoverdetermined Euler-Poisson-Darboux systemWhitham-type equationszero-dispersion limit of the KdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Euler-Poisson-Darboux equations (35Q05)

Related Items (12)

Riemann‐Hilbert problem for the small dispersion limit of the KdV equation and linear overdetermined systems of Euler‐Poisson‐Darboux type ⋮ Superpotentials, quantum parameter space and phase transitions in \( \mathcal{N}=1\) supersymmetric gauge theories ⋮ The initial value problem for the Whitham averaged system ⋮ Exotic wave patterns in Riemann problem of the high‐order Jaulent–Miodek equation: Whitham modulation theory ⋮ On the singular sector of the Hermitian random matrix model in the large \(N\) limit ⋮ Bound to the number of oscillatory phases in the solution of the Whitham-KdV equations ⋮ Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem. ⋮ Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies ⋮ Generation of undular bores in the shelves of slowly-varying solitary waves ⋮ Initial value problem of the Whitham equations for the Camassa-Holm equation ⋮ Evolution of initial discontinuity for the defocusing complex modified KdV equation ⋮ Modulation solutions for the Benjamin-Ono equation

Cites Work

• Method of averaging for two-dimensional integrable equations
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• The small dispersion limit of the korteweg-de vries equation. ii
• The small dispersion limit of the Korteweg-de Vries equation. III
• The small dispersion limit of the Korteweg-de Vries equation. I
• The zero dispersion limit of the korteweg-de vries equation for initial potentials with non-trivial reflection coefficient
• The hyperbolic nature of the zero dispersion Kdv limit
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• Oscillations of the zero dispersion limit of the korteweg‐de vries equation
• Non-linear dispersive waves
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Whitham-type equations and linear overdetermined systems of Euler- Poisson-Darboux type