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- W4300695737 abstract "The present paper deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Our method can be seen as an extension to spatially periodic waves of the theory of solitary waves recently developed in cite{st}. Firstly, our main result do not depend on the parametrization of the periodic wave itself. Secondly, motived 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." @default.
- W4300695737 created "2022-10-04" @default.
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- W4300695737 date "2016-11-15" @default.
- W4300695737 modified "2023-09-30" @default.
- W4300695737 title "Sufficient Conditions for Orbital Stability of Periodic Traveling Waves" @default.
- W4300695737 doi "https://doi.org/10.48550/arxiv.1611.04771" @default.
- W4300695737 hasPublicationYear "2016" @default.
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