Unified approach to KdV modulations

DOI10.1002/cpa.10002zbMath1032.35156arXivnlin/0008007OpenAlexW2108250575MaRDI QIDQ4790254

Stephanos Venakides, Alexander L. Krylov, Gennady A. El

Publication date: 28 January 2003

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0008007

zbMATH Keywords

Whitham modulation equationsKdV-Whitham hierarchyoscillating phaseszero-dispersion KdV

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items

Riemann‐Hilbert problem for the small dispersion limit of the KdV equation and linear overdetermined systems of Euler‐Poisson‐Darboux type ⋮ Whitham systems and deformations ⋮ Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics ⋮ Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation ⋮ Kinetic equation for a soliton gas and Its hydrodynamic reductions ⋮ Resolution of a shock in hyperbolic systems modified by weak dispersion ⋮ Modulated equations of Hamiltonian PDEs and dispersive shocks ⋮ Generation of undular bores in the shelves of slowly-varying solitary waves ⋮ Dispersive shock waves and modulation theory ⋮ Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert problem approach ⋮ Breakdown of the Whitham Modulation Theory and the Emergence of Dispersion ⋮ Undular bore transition in bi-directional conservative wave dynamics

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