An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion
Top Cited Papers
- 17 October 2001
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 87 (19), 194501
- https://doi.org/10.1103/physrevlett.87.194501
Abstract
We use asymptotic analysis and a near-identity normal form transformation from water wave theory to derive a unidirectional nonlinear wave equation that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation. This equation is one order more accurate in asymptotic approximation beyond KdV, yet it still preserves complete integrability via the inverse scattering transform method. Its traveling wave solutions contain both the KdV solitons and the CH peakons as limiting cases.
Keywords
All Related Versions
This publication has 18 references indexed in Scilit:
- On billiard solutions of nonlinear PDEsPhysics Letters A, 1999
- Introduction to Mechanics and SymmetryTexts in Applied Mathematics, 1999
- The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum TheoriesAdvances in Mathematics, 1998
- Euler-Poincaré Models of Ideal Fluids with Nonlinear DispersionPhysical Review Letters, 1998
- A shallow water equation as a geodesic flow on the Bott-Virasoro groupJournal of Geometry and Physics, 1998
- Algebraic Aspects of Integrable SystemsPublished by Springer Nature ,1997
- The geometry of peaked solitons and billiard solutions of a class of integrable PDE'sLetters in Mathematical Physics, 1994
- An integrable shallow water equation with peaked solitonsPhysical Review Letters, 1993
- Applications of Lie Groups to Differential EquationsPublished by Springer Nature ,1993
- Solitons and the Inverse Scattering TransformPublished by Society for Industrial & Applied Mathematics (SIAM) ,1981