A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua.
type: Item
instance of: scholarly article
title: A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua.
zbMATH Open document ID: 1099.37510
DOI: 10.1007/PL00001513
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2000-12-13T00:00:00Z
review text: The author studies the capillary-gravity profiles, which may occur at the interface of two fluids when the fundamental mode and its third harmonic interact with each other. The problem is treated as one in bifurcation theory by transforming it into a nonlinear operator equation between suitable function spaces. Using classical analytic methods and by exploiting the group invariances of the operator, the author describes the solution set of the equation for the selection of values of the parameters present and allows for possible imperfections in the resonance.
reviewed by: Joachim Grispolakis
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 35B99
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 1543028
zbMATH Keywords: capillary-gravity
zbMATH Keywords: mode interaction
zbMATH Keywords: bifurcation
zbMATH Keywords: Lyapunov-Schmidt
zbMATH Keywords: universal unfording
author: Mark C. W. Jones
MaRDI profile type: Publication
full work available at URL: pl00001513
OpenAlex ID: W2005223900
description: scientific article; zbMATH DE number 1543028