Compacton and generalized kink wave solutions of the CH–DP equation

2010 ◽  
Vol 215 (11) ◽  
pp. 4028-4039 ◽  
Author(s):  
Shaolong Xie ◽  
Lin Wang
Keyword(s):  
Wave Solutions ◽  
Kink Wave

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.

Smooth Exact Traveling Wave Solutions Determined by Singular Nonlinear Traveling Wave Systems: Two Models

2019 ◽  
Vol 29 (04) ◽  
pp. 1950047
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Shengfu Deng
Keyword(s):  
Traveling Wave ◽  
Singular System ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Regular System ◽  
Wave System ◽  
Optical Metamaterials ◽  
Wave Solutions ◽  
Straight Line ◽  
Kink Wave

For a singular nonlinear traveling wave system of the first class, if there exist two node points of the associated regular system in the singular straight line, then the dynamics of the solutions of the singular system will be very complex. In this paper, two representative nonlinear traveling wave system models (namely, the traveling wave system of Green–Naghdi equations and the traveling wave system of the Raman soliton model for optical metamaterials) are investigated. It is shown that, if there exist two node points of the associated regular system in the singular straight line, then the singular system has no peakon, periodic peakon and compacton solutions, but rather, it has smooth periodic wave, solitary wave and kink wave solutions.

scholarly journals Lump-Type Wave and Interaction Solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Chuanjian Wang ◽  
Hui Fang
Keyword(s):  
Wave Solution ◽  
Solitary Wave Solutions ◽  
Kink Wave Solution ◽  
Type Wave ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Kink Wave ◽  
Hermitian Quadratic Form

Lump-type wave solution of the Bogoyavlenskii–Kadomtsev–Petviashvili equation is constructed by using the bilinear structure and Hermitian quadratic form. The dynamical behaviors of lump-type wave solution are investigated and presented analytically and graphically. Furthermore, we discuss the interaction between a lump-type wave and a kink wave solution. Absorb-emit interaction between two kinds of solitary wave solutions is shown. This kind of interaction solution can be regarded as a lump-type wave which propagates on the kink wave background.

BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED TWO-COMPONENT CAMASSA–HOLM EQUATION

2012 ◽  
Vol 22 (12) ◽  
pp. 1250305 ◽  
Author(s):  
JIBIN LI ◽  
ZHIJUN QIAO
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Breaking Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Kink Wave

In this paper, we apply the method of dynamical systems to a generalized two-component Camassa–Holm system. Through analysis, we obtain solitary wave solutions, kink and anti-kink wave solutions, cusp wave solutions, breaking wave solutions, and smooth and nonsmooth periodic wave solutions. To guarantee the existence of these solutions, we give constraint conditions among the parameters associated with the generalized Camassa–Holm system. Choosing some special parameters, we obtain exact parametric representations of the traveling 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.

Periodic kink-wave and kinky periodic-wave solutions for the Jimbo–Miwa equation

2008 ◽  
Vol 372 (38) ◽  
pp. 5984-5986 ◽  
Author(s):  
Zhengde Dai ◽  
Jun Liu ◽  
Xiping Zeng ◽  
Zhenjiang Liu
Keyword(s):  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave

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.

BIFURCATIONS OF TRAVELING WAVE SOLUTIONS IN A MICROSTRUCTURED SOLID MODEL

2013 ◽  
Vol 23 (01) ◽  
pp. 1350009 ◽  
Author(s):  
JIBIN LI ◽  
GUANRONG CHEN
Keyword(s):  
Traveling Wave ◽  
Wave Equations ◽  
Traveling Wave Solutions ◽  
Homoclinic Orbits ◽  
Phase Portraits ◽  
Solid Model ◽  
Wave System ◽  
Bounded Solutions ◽  
Wave Solutions ◽  
Kink Wave

The traveling wave system of a microstructured solid model belongs to the second class of singular traveling wave equations studied in [Li et al., 2009]. In this paper, by using methods from dynamical systems theory, bifurcations of phase portraits of such a traveling wave system are analyzed in its corresponding parameter space. The existence of kink wave solutions and uncountably infinitely many bounded solutions is proved. Moreover, the exact parametric representations of periodic solutions and homoclinic orbits are obtained.

Sign in / Sign up

Export Citation Format

Share Document