Communications in Mathematical Sciences

Volume 18 (2020)

Number 3

Periodic traveling-wave solutions for regularized dispersive equations: sufficient conditions for orbital stability with applications

Pages: 613 – 634

DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n3.a2

Authors

Fabrício Cristófani (Instituto de Matemática, Estatística e Computação Científica (IMECC), Universidade Estadual de Campinas (UNICAMP), Campinas, SP, Brazil)

Fábio Natali (Departamento de Matemática, Universidade Estadual de Maringá, PR, Brazil)

Ademir Pastor (Instituto de Matemática, Estatística e Computação Científica (IMECC), Universidade Estadual de Campinas (UNICAMP), Campinas, SP, Brazil)

Abstract

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.

Keywords

orbital stability, regularized dispersive equation, periodic waves

2010 Mathematics Subject Classification

35B10, 35B35, 76B15

Full Text (PDF format)

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