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

2020 ◽  
Vol 18 (3) ◽  
pp. 613-634
Author(s):  
Fabrício Cristófani ◽  
Fábio Natali ◽  
Ademir Pastor
Keyword(s):  
Traveling Wave ◽  
Sufficient Conditions ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Dispersive Equations ◽  
Wave Solutions ◽  
Periodic Traveling Wave

ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED

2021 ◽  
pp. 1-23
Author(s):  
FÁBIO NATALI ◽  
SABRINA AMARAL
Keyword(s):  
Traveling Wave ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Spectral Stability ◽  
Dispersive Equations ◽  
Periodic Waves ◽  
General Proof ◽  
Wave Solutions ◽  
Periodic Traveling Wave

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.

Orbital stability of periodic traveling wave solutions for the Kawahara equation

2017 ◽  
Vol 58 (5) ◽  
pp. 051504 ◽  
Author(s):  
Thiago Pinguello de Andrade ◽  
Fabrício Cristófani ◽  
Fábio Natali
Keyword(s):  
Traveling Wave ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Kawahara Equation ◽  
Wave Solutions ◽  
Periodic Traveling Wave

scholarly journals Orbital stability of periodic traveling-wave solutions for the log-KdV equation

2017 ◽  
Vol 263 (5) ◽  
pp. 2630-2660 ◽  
Author(s):  
Fábio Natali ◽  
Ademir Pastor ◽  
Fabrício Cristófani
Keyword(s):  
Traveling Wave ◽  
Kdv Equation ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Periodic Traveling Wave
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