scholarly journals Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhengyong Ouyang
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Periodic Waves ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

We use bifurcation method of dynamical systems to study exact traveling wave solutions of a nonlinear evolution equation. We obtain exact explicit expressions of bell-shaped solitary wave solutions involving more free parameters, and some existing results are corrected and improved. Also, we get some new exact periodic wave solutions in parameter forms of the Jacobian elliptic function. Further, we find that the bell-shaped waves are limits of the periodic waves in some sense. The results imply that we can deduce bell-shaped waves from periodic waves for some nonlinear evolution equations.

Explicit, periodic and dispersive soliton solutions to the conformable time-fractional Wu–Zhang system

2021 ◽  
pp. 2150417
Author(s):  
Kalim U. Tariq ◽  
Mostafa M. A. Khater ◽  
Muhammad Younis
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Conformable Fractional Derivative ◽  
Physical Behavior ◽  
Wave Solutions

In this paper, some new traveling wave solutions to the conformable time-fractional Wu–Zhang system are constructed with the help of the extended Fan sub-equation method. The conformable fractional derivative is employed to transform the fractional form of the system into ordinary differential system with an integer order. Some distinct types of figures are sketched to illustrate the physical behavior of the obtained solutions. The power and effective of the used method is shown and its ability for applying different forms of nonlinear evolution equations is also verified.

The Periodic Wave Solutions for Two Nonlinear Evolution Equations

2003 ◽  
Vol 40 (2) ◽  
pp. 129-132 ◽  
Author(s):  
Zhang Jin-Liang ◽  
Wang Ming-Liang ◽  
Cheng Dong-Ming ◽  
Fang Zong-De
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Periodic Wave Solutions ◽  
Wave Solutions

scholarly journals Traveling wave solutions of some nonlinear evolution equations

2015 ◽  
Vol 54 (2) ◽  
pp. 263-269 ◽  
Author(s):  
Rafiqul Islam ◽  
Kamruzzaman Khan ◽  
M. Ali Akbar ◽  
Md. Ekramul Islam ◽  
Md. Tanjir Ahmed
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions

scholarly journals The Traveling Wave Solutions and Their Bifurcations for the BBM-LikeB(m,n)Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Shaoyong Li ◽  
Zhengrong Liu
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Blow Up ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solution ◽  
Simulation Approach ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

We investigate the traveling wave solutions and their bifurcations for the BBM-likeB(m,n)equationsut+αux+β(um)x−γ(un)xxt=0by using bifurcation method and numerical simulation approach of dynamical systems. Firstly, for BBM-likeB(3,2)equation, we obtain some precise expressions of traveling wave solutions, which include periodic blow-up and periodic wave solution, peakon and periodic peakon wave solution, and solitary wave and blow-up solution. Furthermore, we reveal the relationships among these solutions theoretically. Secondly, for BBM-likeB(4,2)equation, we construct two periodic wave solutions and two blow-up solutions. In order to confirm the correctness of these solutions, we also check them by software Mathematica.

CONSTRUCTING FAMILIES TRAVELING WAVE SOLUTIONS IN TERMS OF SPECIAL FUNCTION FOR THE ASYMMETRIC NIZHNIK–NOVIKOV–VESSELOV EQUATION

2004 ◽  
Vol 15 (04) ◽  
pp. 595-606 ◽  
Author(s):  
YONG CHEN ◽  
QI WANG
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Special Function ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Algebraic Method ◽  
Nonlinear Evolution Equations ◽  
Symbolic System ◽  
Wave Solutions

By means of a more general ansatz and the computerized symbolic system Maple, a generalized algebraic method to uniformly construct solutions in terms of special function of nonlinear evolution equations (NLEEs) is presented. We not only successfully recover the previously-known traveling wave solutions found by Fan's method, but also obtain some general traveling wave solutions in terms of the special function for the asymmetric Nizhnik–Novikov–Vesselov equation.

Sign in / Sign up

Export Citation Format

Share Document