A Variety of Exact Periodic Wave and Solitary Wave Solutions for the Coupled Higgs Equation

2012 ◽  
Vol 67 (10-11) ◽  
pp. 545-549 ◽  
Author(s):  
Houria Trikia ◽  
Abdul-Majid Wazwazb
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Higgs Field ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Jacobi Elliptic Function Expansion

In this work, the coupled Higgs field equation is studied. The extended Jacobi elliptic function expansion methods are efficiently employed to construct the exact periodic solutions of this model. As a result, many exact travelling wave solutions are obtained which include new shock wave solutions or kink-shaped soliton solutions, solitary wave solutions or bell-shaped soliton solutions, and combined solitary wave solutions are formally obtained.

scholarly journals Extended Jacobi Elliptic Function Expansion Method to the ZK-MEW Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Weimin Zhang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Function Expansion ◽  
Jacobi Elliptic Function Expansion

The extended Jacobi elliptic function expansion method is applied for Zakharov-Kuznetsov-modified equal-width (ZK-MEW) equation. With the aid of symbolic computation, we construct some new Jacobi elliptic doubly periodic wave solutions and the corresponding solitary wave solutions and triangular functional (singly periodic) solutions.

scholarly journals Bifurcations and Parametric Representations of Peakon, Solitary Wave and Smooth Periodic Wave Solutions for a Two-Component Degasperis-Procesi Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Bin He ◽  
Qing Meng ◽  
Jinhua Zhang
Keyword(s):  
Dynamical Systems ◽  
Solitary Wave ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Phase Portraits ◽  
Travelling Wave Solutions ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Two Component

By using the bifurcation method of dynamical systems and the method of phase portraits analysis, we consider a two-component Degasperis-Procesi equation:mt=-3mux-mxu+kρρx,  ρt=-ρxu+2ρux,the existence of the peakon, solitary wave and smooth periodic wave is proved, and exact parametric representations of above travelling wave solutions are obtained in different parameter regions.

Exact single travelling wave solutions to the fractional perturbed Gerdjikov–Ivanov equation in nonlinear optics

2021 ◽  
pp. 2150377
Author(s):  
Xiang Xiao ◽  
Zhixiang Yin
Keyword(s):  
Solitary Wave ◽  
Periodic Solutions ◽  
Travelling Wave ◽  
Polynomial Method ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Triangular Function ◽  
Almost All

In this paper, exact single travelling wave solutions to the nonlinear fractional perturbed Gerdjikov–Ivanov equation are captured by the complete discrimination system for polynomial method and the trial equation method. In the classification, we can find out the original equation has rational function solutions, solitary wave solutions, triangular function periodic solutions, and elliptic function periodic solutions, which are normally very difficult to be obtained by other methods. In particular, the concrete parameters are set to show that the solutions in the classification can be realized in almost all cases.

scholarly journals Periodic Loop Solutions and Their Limit Forms for the Kudryashov-Sinelshchikov Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Bin He ◽  
Qing Meng ◽  
Jinhua Zhang ◽  
Yao Long
Keyword(s):  
Dynamical Systems ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Phase Portraits ◽  
Travelling Wave Solutions ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

The Kudryashov-Sinelshchikov equation is studied by using the bifurcation method of dynamical systems and the method of phase portraits analysis. We show that the limit forms of periodic loop solutions contain loop soliton solutions, smooth periodic wave solutions, and periodic cusp wave solutions. Also, some new exact travelling wave solutions are presented through some special phase orbits.

Exact Periodic Solitary Wave and Double Periodic Wave Solutions for the (2+1)-Dimensional Korteweg-de Vries Equation

2009 ◽  
Vol 64 (9-10) ◽  
pp. 609-614 ◽  
Author(s):  
Changfu Liu ◽  
Zhengde Dai
Keyword(s):  
Solitary Wave ◽  
Function Method ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Trial Function Method ◽  
A New Technique

A new technique, the extended ansatz function method, is proposed to seek periodic solitary wave solutions of integrable systems. Exact periodic solitary wave solutions for the (2+1)-dimensional Korteweg-de Vries (KdV) equation are obtained by using this technique. By using the trial function method, Jacobi elliptic function double periodic solutions are also constructed for this equation. This result shows that there exist periodic solitary waves in the different directions for the (2+1)- dimensional KdV equation

scholarly journals Periodic and Solitary Wave Solutions to the Fornberg-Whitham Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Jiangbo Zhou ◽  
Lixin Tian
Keyword(s):  
Solitary Wave ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Two Parameters ◽  
Whitham Equation

New travelling wave solutions to the Fornberg-Whitham equationut−uxxt+ux+uux=uuxxx+3uxuxxare investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.

scholarly journals Soliton solutions and periodic solutions for two models arises in mathematical physics

2021 ◽  
Vol 7 (3) ◽  
pp. 4439-4458
Author(s):  
F. A. Mohammed ◽  
◽  
Mohammed K. Elboree ◽  
Keyword(s):  
Soliton Solutions ◽  
Higgs Field ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Mathematical Methods ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kudryashov Method ◽  
Kink Wave ◽  
Cubic Nonlinear Schrödinger Equation

<abstract><p>We aimed in this paper to acquire the periodic wave solutions and soliton solutions and other solutions such as kink-wave solutions for the cubic nonlinear Schrödinger equation with repulsive delta potential ($ \delta $-NLSE) and complex coupled Higgs field equation via two mathematical methods Jacobi elliptic function method and generalized Kudryashov method. Some of these solutions are degenerated to solitary wave solutions and periodic wave solutions in the limit case. We also gave the meaning of these solutions physically and the numerical simulation by some figures.</p></abstract>

scholarly journals Jacobian Elliptic Wave Solutions for the Wadati–Segur–Ablowitz Equation

1997 ◽  
Vol 11 (23) ◽  
pp. 2849-2854 ◽  
Author(s):  
C. G. R. Teh ◽  
W. K. Koo ◽  
B. S. Lee
Keyword(s):  
Solitary Wave ◽  
Wave Train ◽  
Travelling Wave ◽  
Amplitude Equation ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By a mere variation of the Jacobian elliptic parameter k2 from zero to one, these solutions are transformed from a trivial one to the known solitary wave solutions.1,2

PERIODIC WAVE SOLUTIONS FOR POCHHAMMER–CHREE EQUATION WITH FIVE ORDER NONLINEAR TERM AND THEIR RELATIONSHIP WITH SOLITARY WAVE SOLUTIONS

2010 ◽  
Vol 24 (19) ◽  
pp. 3769-3783 ◽  
Author(s):  
WEIGUO ZHANG ◽  
YAN ZHAO ◽  
GANG LIU ◽  
TONGKE NING
Keyword(s):  
Solitary Wave ◽  
Nonlinear Term ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Systematic Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Fifth Order ◽  
The Given

In this paper, periodic wave solutions for Pochhammer–Chree equation (PC-equation) with fifth order nonlinear term and their relationship with solitary wave solutions are studied. By designing innovative structure of solution, sixteen bounded periodic wave solutions in fractional form of Jacobi elliptic function (JEF) for PC-equation are given. Furthermore, global phase figure in the plane of the traveling solution for the PC-equation are obtained through dynamic systematic method, we indicate the region in the phase where the given sixteen solutions for PC-equation belong to. We find that two couples of these solutions change into two bell profile solitary wave solutions as k → 1 and four solutions change into four periodic wave solutions in fractional form of cosine function as k → 0. Finally, four figures are shown to describe the evolvement from periodic wave solutions to bell profile solitary wave solutions as k → 1.

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