scholarly journals Traveling wave solutions of compressible fluid equations and orbital stability

AIP Advances ◽  
2015 ◽  
Vol 5 (11) ◽  
pp. 117148
Author(s):  
Xiang Li ◽  
Weiguo Zhang ◽  
Zhengming Li
Keyword(s):  
Compressible Fluid ◽  
Traveling Wave ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Fluid Equations

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.

scholarly journals Orbital Stability of Solitary Traveling Waves of Moderate Amplitude

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Zhengyong Ouyang
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Water Regime ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Stability Theorem ◽  
Hamiltonian Form ◽  
Free Surface Waves ◽  
Wave Solutions ◽  
Invariants Of Motion

We consider the orbital stability of solitary traveling wave solutions of an equation describing the free surface waves of moderate amplitude in the shallow water regime. Firstly, we rewrite this equation in Hamiltonian form and construct two invariants of motion. Then using the abstract stability theorem of solitary waves proposed by Grillakis et al. (1987), we prove that the solitary traveling waves of the equation under consideration are orbital stable.

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
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