Deeper investigations of the (4 + 1)-dimensional Fokas and (2 + 1)-dimensional Breaking soliton equations

2020 ◽  
Vol 34 (17) ◽  
pp. 2050152
Author(s):  
Haci Mehmet Baskonus ◽  
Ajay Kumar ◽  
Ashok Kumar ◽  
Wei Gao
Keyword(s):  
Analytical Method ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Bright Soliton ◽  
Hyperbolic Functions ◽  
Soliton Equations

The main aim of this paper is to investigate the various dimensional nonlinear Fokas and Breaking soliton equations via a powerful analytical method, namely, sine-Gordon expansion method. Many new solutions such as complex combined dark-bright soliton solutions, singular and hyperbolic functions are derived. Choosing the suitable values of these parameters, various novel simulations are also plotted. Such results explain the wave behavior of the governing models, physically.

scholarly journals Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Bright Soliton ◽  
New Wave ◽  
Wave Patterns

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.

New bright soliton solutions for Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equations and bidirectional propagation of water wave surface

2021 ◽  
Author(s):  
S. Saha Ray ◽  
Shailendra Singh
Keyword(s):  
Water Wave ◽  
Soliton Solutions ◽  
Fluid Flows ◽  
Wave Model ◽  
Expansion Method ◽  
Bright Soliton ◽  
Wave Surface ◽  
Model Equations ◽  
Bidirectional Propagation ◽  
Truncated Painlevé Expansion

The governing equations for fluid flows, i.e. Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) model equations represent a water wave model. These model equations describe the bidirectional propagating water wave surface. In this paper, an auto-Bäcklund transformation is being generated by utilizing truncated Painlevé expansion method for the considered equation. This paper determines the new bright soliton solutions for [Formula: see text] and [Formula: see text]-dimensional nonlinear KP-BBM equations. The simplified version of Hirota’s technique is utilized to infer new bright soliton solutions. The results are plotted graphically to understand the physical behavior of solutions.

scholarly journals Complex Patterns to the (3+1)-Dimensional B-type Kadomtsev-Petviashvili-Boussinesq Equation

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 17 ◽  
Author(s):  
Juan Luis García Guirao ◽  
H. M. Baskonus ◽  
Ajay Kumar ◽  
M. S. Rawat ◽  
Gulnur Yel
Keyword(s):  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Bright Soliton ◽  
Wave Patterns ◽  
Complex Patterns

This paper presents many new complex combined dark-bright soliton solutions obtained with the help of the accurate sine-Gordon expansion method to the B-type Kadomtsev-Petviashvili-Boussinesq equation with binary power order nonlinearity. With the use of some computational programs, we plot many new surfaces of the results obtained in this paper. In addition, we present the interactions between complex travelling wave patterns and their solitons.

The (G'/G,1/G)-Expansion Method for Solving the (2+1)-Dimensional Breaking Soliton Equations

2013 ◽  
Vol 787 ◽  
pp. 1006-1010
Author(s):  
Yun Jie Yang ◽  
Yun Mei Zhao ◽  
Yan He
Keyword(s):  
Rational Functions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Soliton Equations ◽  
Wave Solutions

In this paper, the-expansion method is applied to construct more general exact travelling solutions of the (2+1)-dimensional breaking soliton equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions.

A series of complexiton soliton solutions for nonlinear Jaulent—Miodek PDEs using the Riccati equations method

2011 ◽  
Vol 141 (5) ◽  
pp. 1001-1015 ◽  
Author(s):  
E. M. E. Zayed ◽  
Khaled A. Gepreel
Keyword(s):  
Rational Function ◽  
Symbolic Computation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Riccati Equations ◽  
Hyperbolic Function ◽  
Periodic Functions ◽  
Hyperbolic Functions ◽  
Hyperbolic Function Solutions ◽  
Triangular Function

We use the extended multiple Riccati equations expansion method to construct a series of double-soliton-like solutions, double triangular function solutions and complexiton soliton solutions for nonlinear Jaulent-Miodek PDEs. With the help of symbolic computation using Maple and Mathematica, we obtain many new types of complexiton soliton solutions, i.e. various combinations of trigonometric periodic functions and hyperbolic function solutions, various combinations of trigonometric periodic functions and rational function solutions, and various combinations of hyperbolic functions and rational function solutions.

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.

Analytical study of exact solutions of the nonlinear Korteweg–de Vries equation with space–time fractional derivatives

2018 ◽  
Vol 32 (02) ◽  
pp. 1850012 ◽  
Author(s):  
Jiangen Liu ◽  
Yufeng Zhang
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Space Time ◽  
Strong Basis ◽  
De Vries

This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg–de Vries equation with space–time local fractional derivatives. By using the improved [Formula: see text]-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

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