Volume 13, Issue 3, August 2006, Pages 441 - 466
Wave Breaking in a Class of Nonlocal Dispersive Wave Equations
- Hailiang LIU 0
- Corresponding Author
- Hailiang LIU
0Department of Mathematics, Iowa State University
Available Online 10 November 2006.
- https://doi.org/10.2991/jnmp.2006.13.3.8How to use a DOI?
- Nonlocal Dispersive Wave Equations, Wave Breaking, Korteweg de Vries (KdV) equation
- The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which also incorporate physics of short wavelength scales. The model is identified by a renormalization of an infinite dispersive differential operator, followed by further specifications in terms of conservation laws associated with the underlying equation. Several well-known models are thus rediscovered. Wave breaking criteria are obtained for several models including the Burgers-Poisson system, the Camassa-Holm type equation and an Euler-Poisson system. The wave breaking criteria for these models are shown to depend only on the negativity of the initial velocity slope relative to other global quantities.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - Hailiang LIU PY - 2006 DA - 2006/11 TI - Wave Breaking in a Class of Nonlocal Dispersive Wave Equations JO - Journal of Nonlinear Mathematical Physics SP - 441 EP - 466 VL - 13 IS - 3 SN - 1402-9251 UR - https://doi.org/10.2991/jnmp.2006.13.3.8 DO - https://doi.org/10.2991/jnmp.2006.13.3.8 ID - LIU2006 ER -