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Sufficient conditions for orbital stability of periodic traveling waves

Banff International Research Station for Mathematical Innovation and Discovery

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).

Mathematics; Partial differential equations; Dynamical systems and ergodic theory; Functional analysis

video/mp4

Author affiliation: Universidade Estadual de Maringá

2017-12-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64109

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/