Modulation of the Camassa-Holm equation and reciprocal transformations.

DOI10.5802/aif.2142zbMath1116.37042arXivmath-ph/0506042OpenAlexW2105802668MaRDI QIDQ2574188

Tamara Grava, Simonetta Abenda

Publication date: 18 November 2005

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0506042

zbMATH Keywords

Whitham equationsHamiltonian structuresmodulation equationsKorteweg de Vries hierarchy

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 (max. 100)

Whitham systems and deformations ⋮ On solutions of the two-component Camassa-Holm system ⋮ A three-component extension of the Camassa-Holm hierarchy ⋮ Miura-reciprocal transformations and localizable Poisson pencils ⋮ On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data ⋮ On the higher Poisson structures of the Camassa-Holm hierarchy ⋮ Jacobi structures of evolutionary partial differential equations ⋮ Initial value problem of the Whitham equations for the Camassa-Holm equation ⋮ The complete classification of solutions to the Riemann problem of the defocusing complex modified KdV equation ⋮ A small dispersion limit to the Camassa-Holm equation: a numerical study

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Completely integrable systems, Euclidean Lie algebras, and curves
• Method of averaging for two-dimensional integrable equations
• Quasi-periodicity with respect to time of spatially periodic finite-gap solutions of the Camassa-Holm equation
• The initial value problem for the Whitham averaged system
• Integrable systems and symmetric products of curves
• Tri-Hamiltonian structures of Egorov systems of hydrodynamic type
• On the weak Kowalevski-Painlevé property for hyperelliptically separable systems
• Multipeakons and the classical moment problem
• Solution of matrix Riemann-Hilbert problems with quasi-permutation monodromy matrices
• On Whitham's averaging method
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
• Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
• On the scattering problem for the Camassa-Holm equation
• Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• Group velocity and nonlinear dispersive wave propagation
• The small dispersion limit of the Korteweg-de Vries equation. III
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• Bäcklund transformations for hereditary symmetries
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• A shallow water equation on the circle
• Oscillations of the zero dispersion limit of the korteweg‐de vries equation
• The Liouville correspondence between the Korteweg—de Vries and the Camassa‐Holm hierarchies
• Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
• An integrable shallow water equation with peaked solitons
• Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type
• Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems
• A general approach to linear and non-linear dispersive waves using a Lagrangian
• Real-valued algebro-geometric solutions of the Camassa–Holm hierarchy
• On the local systems Hamiltonian in the weakly non-local Poisson brackets
• The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type

This page was built for publication: Modulation of the Camassa-Holm equation and reciprocal transformations.