- The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations
2007/09/06 by Adrian Constantin, David Lannes · 1,023 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Burgers' equation #Camassa–Holm equation #Classical mechanics #Dispersionless equation #Integrable system #Kadomtsev–Petviashvili equation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Partial differential equation #Physics #Quantum mechanics #Relevance (law) #Shallow water equations #Waves and shallow water #math.AP #physics.ao-ph
- The Classical Problem of Water Waves: a Reservoir of Integrable and Nearly-Integrable Equations
2003/01/01 by R. S. Johnson · 80 citations
Physics and Astronomy · Earth and Planetary Sciences · Mathematics · #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #Nonlinear Photonic Systems #Integrable system #Mathematics #Dispersionless equation #Mathematical physics #Camassa–Holm equation #Mathematical analysis #Pure mathematics #Partial differential equation #Kadomtsev–Petviashvili equation
- Camassa–Holm, Korteweg–de Vries and related models for water waves
2002/03/25 by R. S. Johnson · 824 citations
Physics and Astronomy · Earth and Planetary Sciences · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Ocean Waves and Remote Sensing #Camassa–Holm equation #Korteweg–de Vries equation #Mathematics #Mathematical analysis #Context (archaeology) #Independent equation #Shallow water equations #Initial value problem #Dispersionless equation #Physics #Nonlinear system #Differential equation #Kadomtsev–Petviashvili equation #Integrable system #Characteristic equation #Geology
- Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support
1996/02/01 by Peter J. Olver, Philip Rosenau · 821 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Advanced Fiber Laser Technologies #Integrable system #Hamiltonian (control theory) #Mathematical physics #Duality (order theory) #Nonlinear system #Dispersionless equation #Physics #Scaling #Hamiltonian system #Mathematical analysis #Mathematics #Pure mathematics #Quantum mechanics #Kadomtsev–Petviashvili equation #Geometry #Burgers' equation
- A New Integrable Shallow Water Equation
1994/01/01 by Roberto Camassa, Darryl D. Holm, James M. Hyman · 753 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
- The Korteweg-de Vries equation: a historical essay
1981/05/01 by John W. Miles · 201 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Advanced Mathematical Physics Problems #Korteweg–de Vries equation #Physics #Inverse scattering transform #Dispersion relation #Mathematical physics #Dispersionless equation #Inverse scattering problem #Soliton #Nonlinear system #Inverse #Dispersion (optics) #Wave packet #Kadomtsev–Petviashvili equation #Classical mechanics #Mathematical analysis #Scattering #Quantum mechanics #Burgers' equation #Mathematics