Solitary-wave solutions of the Benjamin equation
Considered here is a model equation put forward by Benjamin that governs approximately the evolution of waves on the interface of a two-fluid system in which surface-tension effects cannot be ignored. The principal focus is the traveling-wave solutions called solitary waves, and three aspects will be investigated. A constructive proof of the existence of these waves together with a proof of their stability is developed. Continuation methods are used to generate a scheme capable of numerically approximating these solitary waves. The computer-generated approximations reveal detailed aspects of the structure of these waves. They are symmetric about their crests, but unlike the classical Korteqeg-de Vries solitary waves, they feature a finite number of oscillations. The derivation of the equation is also revisited to get an idea of whether or not these oscillatory waves might actually occur in a natural setting.
- Research Organization:
- Univ. of Oklahoma, Norman, OK (US)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 20005557
- Journal Information:
- SIAM Journal on Applied Mathematics (Society for Industrial and Applied Mathematics), Vol. 59, Issue 6; Other Information: PBD: Oct 1999; ISSN 0036-1399
- Country of Publication:
- United States
- Language:
- English
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