THE EXACT THEORY OF STEADY STATE WAVES ON THE SURFACE OF A HEAVY LIQUID.
Abstract
The existence of periodic progressing waves of finite amplitude on the surface of a heavy liquid of finite or infinite depth is investigated. It is first shown that the problem is equivalent to solving a non-linear integral equation. The existence of solutions of the non-linear integral equation is then proved by expanding the solutions in a perturbation series about the solution of the linearized integral equation, and showing that the perturbation series is convergent for waves of sufficiently small amplitude. The first few terms of the perturbation series are calculated. The use of perturbation series for solving non-linear integral equations is discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1967
- Accession Number
- AD0674454
Entities
People
- A. I. Nekrasov
Organizations
- University of Wisconsin–Madison