BIRS Workshop Lecture Videos
Sufficient conditions for orbital stability of periodic traveling waves Natali, Fabio
The present talk deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Firstly, our main result does not depend on the parametrization of the periodic wave itself. Secondly, motivated by the well known orbital stability criterion for solitary waves, we show that the same criterion holds for periodic waves. In addition, we show that the positiveness of the principal entries of the Hessian matrix related to the ``energy surface function'' are also sufficient to obtain the stability. Consequently, we can establish the orbital stability of periodic waves for several nonlinear dispersive models. We believe our method can be applied in a wide class of evolution equations; in particular it can be extended to regularized dispersive wave equations. This is a joint work with A. Pastor (IMECC/UNICAMP-Brazil) and G. Alves (ULCO-France).
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