About the Explicit Characterization of Hamiltonians of the Camassa-Holm Hierarchy

2005/01/01 by Enrique Loubet · 1 citation
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Algebraic structures and combinatorial models #Hierarchy #Mathematics #Series (stratigraphy) #Characterization (materials science) #Computation #Flow (mathematics) #Motion (physics) #Pure mathematics #Applied mathematics #Algebra over a field #Geometry #Classical mechanics #Physics #Algorithm

paper · pdf · doi:10.2991/jnmp.2005.12.1.11

openalex publication_date 2005/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We present a detailed computation leading to an explicit formula for the fourth Hamitonian in the series of constants of motion with which any flow of the Camassa-Holm hierarchy is equipped, and explain the inherent difficulties in achieving such explicit expressions for invariants higher in the series.

Citations

• A New Integrable Shallow Water Equation
• Breakdown of the Camassa‐Holm equation
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• Fredholm determinants and the Camassa‐Holm hierarchy
• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• The Liouville correspondence between the Korteweg—de Vries and the Camassa‐Holm hierarchies
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Wave breaking for nonlinear nonlocal shallow water equations
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• Geodesic flow on the diffeomorphism group of the circle
• Multipeakons and the Classical Moment Problem

Cited by

• Camassa–Holm equation [wikipedia]