A New Integrable Shallow Water Equation

1994/01/01 by Roberto Camassa, Darryl D. Holm, James M. Hyman · 33 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Ansatz #Burgers' equation #Camassa–Holm equation #Classical mechanics #Coastal and Marine Dynamics #Compressibility #Dispersionless equation #Dispersive partial differential equation #Euler equations #Hamiltonian (control theory) #Integrable system #Kadomtsev–Petviashvili equation #Korteweg–de Vries equation #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Nonlinear Waves and Solitons #Nonlinear system #Ocean Waves and Remote Sensing #Partial differential equation #Physics #Quantum mechanics #Shallow water equations #Waves and shallow water

paper · doi:10.1016/s0065-2156(08)70254-0

crossref issued 1994/01/01 · crossref published 1994/01/01 · crossref published-print 1994/01/01 · openalex publication_date 1994/01/01 · crossref created 2008/11/19 · crossref deposited 2018/12/24 · openalex created_date 2025/10/10 · crossref indexed 2026/08/05 · openalex updated_date 2026/08/08

Citations

• Long waves on a beach

Cited by

• Camassa–Holm, Korteweg–de Vries and related models for water waves
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Traveling wave solutions of the Camassa–Holm equation
• Orbital stability of solitary waves for a shallow water equation
• Geometric Integrability of the Camassa–Holm Equation
• The Camassa–Holm equation for water waves moving over a shear flow
• Multi-symplectic integration of the Camassa–Holm equation
• Integral and integrable algorithms for a nonlinear shallow-water wave equation
• Infinite propagation speed of the Camassa–Holm equation
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
• Initial Boundary Value Problems of the Camassa–Holm Equation
• Blow-up, blow-up rate and decay of the solution of the weakly dissipative Camassa-Holm equation
• Low-Regularity Solutions of the Periodic Camassa–Holm Equation
• A factorization procedure for solving the Camassa–Holm equation
• On the scattering problem for the Camassa-Holm equation
• On solutions of the Camassa-Holm equation
• On the Camassa–Holm equation and a direct method of solution. III. N -soliton solutions
• On the Camassa-Holm equation and a direct method of solution I. Bilinear form and solitary waves
• On the Camassa–Holm equation and a direct method of solution. II. Soliton solutions
• GLOBAL CONSERVATIVE MULTIPEAKON SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Convergence of a Finite Difference Scheme for the Camassa–Holm Equation
• Transformations for the Camassa-Holm Equation, Its High-Frequency Limit and the Sinh-Gordon Equation
• A Convergent Finite Difference Scheme for the Camassa–Holm Equation with General H¹ Initial Data
• Existence time for the Camassa-Holm equation and the critical Sobolev index
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• A convergent numerical scheme for the Camassa--Holm equation based on multipeakons
• Periodic conservative solutions of the Camassa–Holm equation
• Stability for the periodic Camassa-Holm equation
• About the Explicit Characterization of Hamiltonians of the Camassa-Holm Hierarchy
• The Classical Problem of Water Waves: a Reservoir of Integrable and Nearly-Integrable Equations
• On a Completely Integrable Numerical Scheme for a Nonlinear Shallow-Water Wave Equation
• Inverse scattering solutions of the hunter-saxton equation
• Camassa–Holm equation [wikipedia]