Convergence of Periodic Wavetrains in the Limit of Large Wavelength.
Abstract
The korteweg-de Vries equation was originally derived as a model for unidirectional propagation of water waves. This equation possesses a special class of traveling-wave solutions corresponding to surface solitary waves. It also has permanent-wave solutions which are periodic in space, the so-called cnoidal waves. A classical observation of Korteweg and de Vries was that the solitary wave is obtained as a certain limit of cnoidal wavetrains. This results is extended here, in the context of the Korteweg-de Vries equation. It is demonstrated that a general class of solutions of the Korteweg-de Vries equation is obtained as limiting forms of periodic solutions, as the period becomes large. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1981
- Accession Number
- ADA100609
Entities
People
- Jerry L. Bona
Organizations
- University of Wisconsin–Madison