scholarly journals Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case

2010 ◽  
Vol 249 (5) ◽  
pp. 1213-1240 ◽  
Author(s):  
Mathew A. Johnson ◽  
Kevin Zumbrun
Keyword(s):  
Conservation Laws ◽  
Nonlinear Stability ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Viscous Conservation Laws ◽  
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.

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