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.
Submitted April 28, 2003. Published September 17, 2003.
Math Subject Classifications: 35L70, 37J40, 70H08.
Key Words: Kirchhoff equations, orbital stability, Hamiltonian systems, Poincare map, KAM theory.
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