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ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED

Part of: Equations of mathematical physics and other areas of application Infinite-dimensional Hamiltonian systems Incompressible inviscid fluids

Published online by Cambridge University Press:  25 August 2021

FÁBIO NATALI Open the ORCID record for FÁBIO NATALI [Opens in a new window]  and
SABRINA AMARAL Open the ORCID record for SABRINA AMARAL [Opens in a new window]
FÁBIO NATALI
Affiliation:
Departamento de Matemática Universidade Estadual de Maringá, Avenida Colombo 5790 CEP 87020-900, Maringá PR, Brazil [email protected]
SABRINA AMARAL
Affiliation:
Departamento de Matemática Universidade Estadual de Maringá, Avenida Colombo 5790 CEP 87020-900, Maringá PR, Brazil [email protected]
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Abstract

The purpose of this paper is to present an extension of the results in [8]. We establish a more general proof for the moving kernel formula to prove the spectral stability of periodic traveling wave solutions for the regularized Benjamin–Bona–Mahony type equations. As applications of our analysis, we show the spectral instability for the quintic Benjamin–Bona–Mahony equation and the spectral (orbital) stability for the regularized Benjamin–Ono equation.

MSC classification

Primary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Secondary: 37K45: Stability problems 35Q53: KdV-like equations (Korteweg-de Vries)
Type
Article
Information
Nagoya Mathematical Journal , Volume 247 , September 2022 , pp. 471 - 493
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Copyright
© (2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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