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 these simple modes are stable provided that their energy is small enough. Here stable means orbitally stable as solutions of the two-mode system obtained considering initial data with two Fourier components.
Stability of simple modes for a class of Kirchhoff equation
GHISI, MARINA;GOBBINO, MASSIMO
2001-01-01
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 these simple modes are stable provided that their energy is small enough. Here stable means orbitally stable as solutions of the two-mode system obtained considering initial data with two Fourier components.File in questo prodotto:
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