Sufficient Conditions for Orbital Stability of Periodic Traveling Waves

Alves, Giovana; Natali, Fábio; Pastor, Ademir

doi:10.48550/arxiv.1611.04771

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2019

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“…Our main goal in this paper is to establish a new criterion for the orbital stability where it is not necessary to know the positiveness of the associated Hessian matrix neither the Jacobians as determined in [7], [14] and [16]. To do so, instead of considering G as a Lyapunov function, based on the works [2], [26] and [29], we consider the new functional given by…”

Section: Introductionmentioning

confidence: 99%

Periodic Traveling-wave solutions for regularized dispersive equations: Sufficient conditions for orbital stability with applications

Cristófani¹,

Natali²,

Pastor³

2019

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In this paper, we establish a new criterion for the orbital stability of periodic waves related to a general class of regularized dispersive equations. More specifically, we present sufficient conditions for the stability without knowing the positiveness of the associated hessian matrix. As application of our method, we show the orbital stability for the fifth-order model. The orbital stability of periodic waves resulting from a minimization of a convenient functional is also proved.

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