Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem.

DOI10.1016/S0375-9601(96)00667-6zbMath1037.35503OpenAlexW2003115854MaRDI QIDQ1968031

Gennady A. El

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(96)00667-6

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (8)

Unified approach to KdV modulations ⋮ Riemann‐Hilbert problem for the small dispersion limit of the KdV equation and linear overdetermined systems of Euler‐Poisson‐Darboux type ⋮ 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 ⋮ Temporal asymptotics for soliton equations in problems with step initial conditions ⋮ Shock waves in dispersive Eulerian fluids ⋮ Modulation solutions for the Benjamin-Ono equation

Cites Work

• Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models
• The Whitham-type equations and linear overdetermined systems of Euler- Poisson-Darboux type
• Whitham equations in the AKNS scheme
• General solution of the Cauchy problem for the defocusing NLS equation in the Whitham limit
• The zero dispersion limit of the korteweg-de vries equation for initial potentials with non-trivial reflection coefficient
• 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
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• Oscillations of the zero dispersion limit of the korteweg‐de vries equation
• Computing the weak limit of KdV
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