Communications in Mathematical Sciences
Volume 18 (2020)
Periodic traveling-wave solutions for regularized dispersive equations: sufficient conditions for orbital stability with applications
Pages: 613 – 634
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.
orbital stability, regularized dispersive equation, periodic waves
2010 Mathematics Subject Classification
35B10, 35B35, 76B15
F. C. is supported by FAPESP/Brazil grant 2017/20760-0. A. P. is partially supported by CNPq/Brazil grants 402849/2016-7 and 303098/2016-3. F. N. is partially supported by CNPq/Brazil and Fundação Araucária/Brazil grants 304240/2018-4 and 002/2017. The third author would like to express his gratitude to McMaster University for its hospitality and Dmitry E. Pelinovsky for fruitful comments regarding this work.
Received 23 November 2018
Accepted 15 November 2019
Published 30 June 2020