Large energy simple modes for a class of Kirchhoff equations
Date
2003-09-17
Authors
Ghisi, Marina
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
It is well known that the Kirchhoff equation admits infinitely many simple modes, i.e., time periodic solutions with only one Fourier component in the space variable(s). We prove that for some form of the nonlinear term these simple modes are stable provided that their energy is large enough. Here stable means orbitally stable as solutions of the two-modes system obtained considering initial data with two Fourier components.
Description
Keywords
Kirchhoff equations, Orbital stability, Hamiltonian systems, Poincare map, KAM theory
Citation
Ghisi, M. (2003). Large energy simple modes for a class of Kirchhoff equations. <i>Electronic Journal of Differential Equations, 2003</i>(96), pp. 1-24.
Rights
Attribution 4.0 International