Integrable Models of Shallow Water Waves
Abstract
The Korteweg-deVries and the Kadomtsev-Petviashvili (KP) equations both model the evolution of relatively long water waves of moderate amplitude as they propagate in shallow water. Both equations are completely integrable. In this paper we review the derivation of each equation as an approximate model of shallow water waves, and compare their solutions with some of the experimental observations of waves in shallow water. We also describe in detail the family of doubly periodic KP solutions. These are the natural two-dimensonal generalizations of cnoidal waves in one-dimensional; one may think of them as describing 'typical' patterns of nonlinear, two-dimensional waves in shallow water.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1983
- Accession Number
- ADA127816
Entities
People
- Allan Finkel
- Harvey Segur