Doubly periodic wave and folded solitary wave solutions for (2+1)-dimensional higher-order Broer–Kaup equation

2007 ◽  
Vol 31 (1) ◽  
pp. 54-63 ◽  
Author(s):  
Wenhua Huang ◽  
Yulu Liu ◽  
Zhiming Lu
Keyword(s):  
Solitary Wave ◽  
Periodic Wave ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Wave Solutions

TRAVELING WAVES FOR AN INTEGRABLE HIGHER ORDER KDV TYPE WAVE EQUATIONS

2006 ◽  
Vol 16 (08) ◽  
pp. 2235-2260 ◽  
Author(s):  
JIBIN LI ◽  
JIANHONG WU ◽  
HUAIPING ZHU
Keyword(s):  
Solitary Wave ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Periodic Wave ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Planar Dynamical Systems

Using the method of planar dynamical systems to a higher order wave equations of KdV type, the existence of smooth and nonsmooth solitary wave, kink wave and uncountably infinite many periodic wave solutions is proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some spatial conditions, the exact explicit parametric representations of solitary wave solutions are determined.

Traveling Wave Solutions of a Two-Component Dullin–Gottwald–Holm System

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Jiyu Zhong ◽  
Shengfu Deng
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Phase Portraits ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Planar Systems

In this paper, we investigate the traveling wave solutions of a two-component Dullin–Gottwald–Holm (DGH) system. By qualitative analysis methods of planar systems, we investigate completely the topological behavior of the solutions of the traveling wave system, which is derived from the two-component Dullin–Gottwald–Holm system, and show the corresponding phase portraits. We prove the topological types of degenerate equilibria by the technique of desingularization. According to the dynamical behaviors of the solutions, we give all the bounded exact traveling wave solutions of the system, including solitary wave solutions, periodic wave solutions, cusp solitary wave solutions, periodic cusp wave solutions, compactonlike wave solutions, and kinklike and antikinklike wave solutions. Furthermore, to verify the correctness of our results, we simulate these bounded wave solutions using the software maple version 18.

scholarly journals New Exact Solitary Wave Solutions of a Coupled Nonlinear Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
XiaoHua Liu ◽  
CaiXia He
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Sufficient Conditions ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Undetermined Coefficient ◽  
Planar Dynamical Systems

By using the theory of planar dynamical systems to a coupled nonlinear wave equation, the existence of bell-shaped solitary wave solutions, kink-shaped solitary wave solutions, and periodic wave solutions is obtained. Under the different parametric values, various sufficient conditions to guarantee the existence of the above solutions are given. With the help of three different undetermined coefficient methods, we investigated the new exact explicit expression of all three bell-shaped solitary wave solutions and one kink solitary wave solutions with nonzero asymptotic value for a coupled nonlinear wave equation. The solutions cannot be deduced from the former references.

scholarly journals Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Ming Song ◽  
Zhengrong Liu
Keyword(s):  
Dynamical Systems ◽  
Solitary Wave ◽  
Blow Up ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Bbm Equation

We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.

Solitary wave solutions of (2+1)-dimensional Maccari system

2021 ◽  
pp. 2150391
Author(s):  
Ghazala Akram ◽  
Naila Sajid
Keyword(s):  
Nonlinear Optics ◽  
Solitary Wave ◽  
Plasma Physics ◽  
Exact Solutions ◽  
Function Method ◽  
Expansion Method ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this article, three mathematical techniques have been operationalized to discover novel solitary wave solutions of (2+1)-dimensional Maccari system, which also known as soliton equation. This model equation is usually of applicative relevance in hydrodynamics, nonlinear optics and plasma physics. The [Formula: see text] function, the hyperbolic function and the [Formula: see text]-expansion techniques are used to obtain the novel exact solutions of the (2+1)-dimensional Maccari system (arising in nonlinear optics and in plasma physics). Many novel solutions such as periodic wave solutions by [Formula: see text] function method, singular, combined-singular and periodic solutions by hyperbolic function method, hyperbolic, rational and trigonometric solutions by [Formula: see text]-expansion method are obtained. The exact solutions are shown through 3D graphics which present the movement of the obtained solutions.

A Higher Order (2+1)-Dimensional Korteweg-de Vries Equation and Its Exact Solitary Wave Solutions

1990 ◽  
Vol 14 (2) ◽  
pp. 221-224
Author(s):  
Guo-xiang Huang ◽  
Xian-xi Dai ◽  
Sen-yue Lou
Keyword(s):  
Solitary Wave ◽  
Vries Equation ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries

Solitary wave solutions to higher-order traffic flow model with large diffusion

2014 ◽  
Vol 35 (2) ◽  
pp. 167-176
Author(s):  
Xiao-xia Jian ◽  
Peng Zhang ◽  
S. C. Wong ◽  
Dian-liang Qiao ◽  
Kee-choo Choi
Keyword(s):  
Solitary Wave ◽  
Traffic Flow ◽  
Flow Model ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Traffic Flow Model ◽  
Wave Solutions ◽  
Large Diffusion
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