Two new types of nonlocal Boussinesq equations in water waves: Bright and dark soliton solutions

2021 ◽  
Author(s):  
Bang-Qing Li ◽  
Wazwaz Abdul-Majid ◽  
Yu-Lan Ma
Keyword(s):  
Water Waves ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Dark Soliton

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines

2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Auxiliary Equation ◽  
Discussion Section ◽  
Auxiliary Equation Method ◽  
Advantages And Disadvantages

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.

Oblique nonlinear Alfvén waves in strongly magnetized beam plasmas. Part 2. Soliton solutions and integrability

1993 ◽  
Vol 50 (3) ◽  
pp. 457-476 ◽  
Author(s):  
Bernard Deconinck ◽  
Peter Meuris ◽  
Frank Verheest
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Mhd Waves ◽  
Displacement Current ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.

New Dark Soliton Solutions of the KdV Equation

1993 ◽  
Vol 20 (4) ◽  
pp. 493-493
Author(s):  
Zong-Yun Chen ◽  
Nian-Ning Huang
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
The Kdv Equation

scholarly journals New soliton solutions of the system of equations for the ion sound and Langmuir waves

2016 ◽  
Vol 7 (1) ◽  
pp. 42-49
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Sound Wave ◽  
High Frequency ◽  
Ponderomotive Force ◽  
Soliton Solutions ◽  
Langmuir Wave ◽  
Dark Soliton ◽  
System Of Equations ◽  
Langmuir Waves ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM), which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.

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