Accession Number : AD0674454

Title :   THE EXACT THEORY OF STEADY STATE WAVES ON THE SURFACE OF A HEAVY LIQUID.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Nekrasov,A. I.

Report Date : JUL 1967

Pagination or Media Count : 133

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)

Descriptors :   (*HYDRODYNAMICS, *INTEGRAL EQUATIONS), (*WAVE PROPAGATION, LIQUIDS), PERTURBATION THEORY, PERIODIC VARIATIONS, NONLINEAR SYSTEMS, THREE DIMENSIONAL FLOW, CONFORMAL MAPPING, POTENTIAL THEORY, COMPLEX VARIABLES, SERIES(MATHEMATICS), CONVERGENCE, USSR

Subject Categories : Theoretical Mathematics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE