Abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota–Maccari system

2012 ◽  
Vol 85 (6) ◽  
pp. 065011 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Field Equation ◽  
Higgs Field ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions

scholarly journals Bifurcations of Traveling Wave Solutions for the Coupled Higgs Field Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Shengqiang Tang ◽  
Shu Xia
Keyword(s):  
Field Equation ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Higgs Field ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions

By using the bifurcation theory of dynamical systems, we study the coupled Higgs field equation and the existence of new solitary wave solutions, and uncountably infinite many periodic wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All exact explicit parametric representations of the above waves are determined.

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 New Types of Doubly Periodic Standing Wave Solutions for the Coupled Higgs Field Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Gui-qiong Xu
Keyword(s):  
Field Equation ◽  
Standing Wave ◽  
Higgs Field ◽  
Jacobi Elliptic Function ◽  
Bilinear Method ◽  
Wave Solutions ◽  
New Type ◽  
Function Expression ◽  
Parameter Values ◽  
Hirota Bilinear

Based on the Hirota bilinear method and theta function identities, we obtain a new type of doubly periodic standing wave solutions for a coupled Higgs field equation. The Jacobi elliptic function expression and long wave limits of the periodic solutions are also presented. By selecting appropriate parameter values, we analyze the interaction properties of periodic-periodic waves and periodic-solitary waves by some figures.

scholarly journals Optical solutions and other solutions for Radhakrishnan-Kundu-Laksmannan equation by using improved modified extended tanh-function method

2021 ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El–Barkouky ◽  
Hamdy Ahmed ◽  
Rabab M. I. El-Hassani ◽  
Ahmed H. Arnous
Keyword(s):  
Optical Fiber ◽  
Function Method ◽  
Pulse Propagation ◽  
Periodic Wave ◽  
Optical Fiber Communications ◽  
Periodic Wave Solutions ◽  
Bright Solitons ◽  
Wave Solutions ◽  
Elliptic Solutions ◽  
Fiber Communications

Abstract This paper studies Radhakrishnan-Kundu-Laksmannan equation which is used to describe the pulse propagation in optical fiber communications. By using improved modified extended tanh-function method various types of solutions are extracted such as bright solitons, singular solitons, singular periodic wave solutions, Jacobi elliptic solutions, periodic wave solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some of the obtained solutions are represented graphically.

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