Traveling Wave Solutions for a Coupled KdV Equations

2014 ◽  
Vol 4 (8) ◽  
pp. 1027-1034
Author(s):  
Ye Zhang
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Coupled Kdv Equations

ON A CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS (II): AN EXAMPLE OF GCKdV EQUATIONS

2009 ◽  
Vol 19 (06) ◽  
pp. 1995-2007 ◽  
Author(s):  
JIBIN LI ◽  
YI ZHANG ◽  
XIAOHUA ZHAO
Keyword(s):  
Traveling Wave ◽  
Wave Equations ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Kink Wave ◽  
Coupled Kdv Equations

By using the method of dynamical systems, we continuously study the dynamical behavior for the first class of singular nonlinear traveling wave systems. As an example, the traveling wave solutions for a generalized coupled KdV equations are discussed. Exact explicit parametric representations of solitary wave solutions, periodic wave solutions and kink wave solutions are given.

scholarly journals Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Zhao Li ◽  
Peng Li ◽  
Tianyong Han
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Solitary Wave Solutions ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Coupled Kdv Equations

In this paper, the bifurcation, phase portraits, traveling wave solutions, and stability analysis of the fractional generalized Hirota–Satsuma coupled KdV equations are investigated by utilizing the bifurcation theory. Firstly, the fractional generalized Hirota–Satsuma coupled KdV equations are transformed into two-dimensional Hamiltonian system by traveling wave transformation and the bifurcation theory. Then, the traveling wave solutions of the fractional generalized Hirota–Satsuma coupled KdV equations corresponding to phase orbits are easily obtained by applying the method of planar dynamical systems; these solutions include not only the bell solitary wave solutions, kink solitary wave solutions, anti-kink solitary wave solutions, and periodic wave solutions but also Jacobian elliptic function solutions. Finally, the stability criteria of the generalized Hirota–Satsuma coupled KdV equations are given.

scholarly journals Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
A. R. Seadawy ◽  
K. El-Rashidy
Keyword(s):  
Solitary Wave ◽  
Traveling Wave Solutions ◽  
Coupled System ◽  
Solitary Wave Solutions ◽  
Coupled Partial Differential Equations ◽  
Extended Tanh Method ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Tanh Method ◽  
Coupled Kdv Equations

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable.

Two types of traveling wave solutions to burgers-KdV equations

2000 ◽  
Vol 21 (10) ◽  
pp. 1119-1122 ◽  
Author(s):  
Zhang Yu-feng ◽  
Zhang Hong-qing
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Kdv Equations ◽  
Wave Solutions
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