ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED LONG-SHORT WAVE EQUATIONS

2019 ◽  
Vol 9 (6) ◽  
pp. 2389-2408 ◽  
Author(s):  
Xiaoxiao Zheng ◽  
◽  
Jie Xin ◽  
Xiaoming Peng ◽  
Keyword(s):  
Traveling Wave ◽  
Wave Equations ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Short Wave ◽  
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

scholarly journals Fundamental solutions for the long–short-wave interaction system

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1093-1099
Author(s):  
Mustafa Inc ◽  
Samia Zaki Hassan ◽  
Mahmoud Abdelrahman ◽  
Reem Abdalaziz Alomair ◽  
Yu-Ming Chu
Keyword(s):  
Fluid Mechanics ◽  
Traveling Wave ◽  
Inverse Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Wave Interaction ◽  
Fundamental Solutions ◽  
Short Wave ◽  
Wave Solutions ◽  
Physical Environments

Abstract In this article, the system for the long–short-wave interaction (LS) system is considered. In order to construct some new traveling wave solutions, He’s semi-inverse method is implemented. These solutions may be applicable for some physical environments, such as physics and fluid mechanics. These new solutions show that the proposed method is easy to apply and the proposed technique is a very powerful tool to solve many other nonlinear partial differential equations in applied science.

Sign in / Sign up

Export Citation Format

Share Document