The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation

2010 ◽  
Vol 126 (1) ◽  
pp. 17-48 ◽  
Author(s):  
B. Deconinck ◽  
M Nivala
Keyword(s):  
Stability Analysis ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Mkdv Equation ◽  
Wave Solutions ◽  
Periodic Traveling Wave ◽  
The Stability

Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics

2020 ◽  
Vol 34 (29) ◽  
pp. 2050282
Author(s):  
Asıf Yokuş ◽  
Doğan Kaya
Keyword(s):  
Traveling Wave ◽  
Numerical Solutions ◽  
Traveling Wave Solutions ◽  
Transformation Method ◽  
Mkdv Equation ◽  
Traveling Wave Solution ◽  
Von Neumann ◽  
Wave Solutions ◽  
De Vries ◽  
The Stability

The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.

scholarly journals Stability Analysis and Assortment of Exact Traveling Wave Solutions for the (2+1)-Dimensional Boiti-Leon-Pempinelli System

2021 ◽  
pp. 2393-2400
Author(s):  
Mizal H. Alobaidi ◽  
Wafaa M. Taha ◽  
Ali H. Hazza ◽  
Pelumi E. Oguntunde
Keyword(s):  
Stability Analysis ◽  
Traveling Wave ◽  
Physical Meaning ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Exact Results ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
The Stability

     In this research, the Boiti–Leon–Pempinelli (BLP) system was used to understand the physical meaning of exact and solitary traveling wave solutions. To establish modern exact results, considered. In addition, the results obtained were compared with those obtained by using other existing methods, such as the standard hyperbolic tanh function method, and the stability analysis for the results was discussed.

scholarly journals Stability for the periodic Camassa-Holm equation

2005 ◽  
Vol 97 (2) ◽  
pp. 188 ◽  
Author(s):  
Jonatan Lenells
Keyword(s):  
Periodic Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Holm Equation ◽  
Periodic Traveling Wave ◽  
The Stability

We use integrability to prove the stability of smooth periodic solutions of the Camassa-Holm equation. In particular, the smooth periodic traveling wave solutions are shown to be orbitally stable.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

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 All exact traveling wave solutions of the combined KdV-mKdV equation

2014 ◽  
Vol 2014 (1) ◽  
pp. 261 ◽  
Author(s):  
Yong Huang ◽  
Yonghong Wu ◽  
Fanning Meng ◽  
Wenjun Yuan
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Mkdv Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions
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