Stability of Periodic Traveling Wave Solutions to the Kawahara Equation

2018 ◽  
Vol 17 (4) ◽  
pp. 2761-2783 ◽  
Author(s):  
Olga Trichtchenko ◽  
Bernard Deconinck ◽  
Richard Kollár
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Kawahara Equation ◽  
Wave Solutions ◽  
Periodic Traveling Wave

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

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 Anti-periodic traveling wave solutions to a class of higher-order Kadomtsev-Petviashvili-Burgers equations

1994 ◽  
Vol 7 (1) ◽  
pp. 1-12
Author(s):  
Sergiu Aizicovici ◽  
Yun Gao ◽  
Shih-Liang Wen
Keyword(s):  
Traveling Wave ◽  
Continuous Dependence ◽  
Traveling Wave Solutions ◽  
Higher Order ◽  
Two Dimensional ◽  
Burgers Equations ◽  
Wave Solutions ◽  
Periodic Traveling Wave ◽  
Continuous Dependence On Data

We discuss the existence, uniqueness, and continuous dependence on data, of anti-periodic traveling wave solutions to higher order two-dimensional equations of Korteweg-deVries type.

scholarly journals Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation

2000 ◽  
Vol 24 (6) ◽  
pp. 371-377 ◽  
Author(s):  
Kenneth L. Jones ◽  
Xiaogui He ◽  
Yunkai Chen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Integral Equations ◽  
Traveling Wave ◽  
Vries Equation ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
De Vries ◽  
Periodic Traveling Wave

This paper is concerned with periodic traveling wave solutions of the forced generalized nearly concentric Korteweg-de Vries equation in the form of(uη+u/(2η)+[f(u)]ξ+uξξξ)ξ+uθθ/η2=h0. The authors first convert this equation into a forced generalized Kadomtsev-Petviashvili equation,(ut+[f(u)]x+uxxx)x+uyy=h0, and then to a nonlinear ordinary differential equation with periodic boundary conditions. An equivalent relationship between the ordinary differential equation and nonlinear integral equations with symmetric kernels is established by using the Green's function method. The integral representations generate compact operators in a Banach space of real-valued continuous functions. The Schauder's fixed point theorem is then used to prove the existence of nonconstant solutions to the integral equations. Therefore, the existence of periodic traveling wave solutions to the forced generalized KP equation, and hence the nearly concentric KdV equation, is proved.

Jacobian elliptic periodic traveling wave solutions for Biswas–Milovic equation

Optik ◽  
2017 ◽  
Vol 131 ◽  
pp. 582-587 ◽  
Author(s):  
S.T.R. Rizvi ◽  
S. Bashir ◽  
K. Ali ◽  
S. Ahmad
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Periodic Traveling Wave
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