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.

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.

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 BRIGHT AND DARK SOLITON SOLUTIONS OF THE (2 + 1)-DIMENSIONAL EVOLUTION EQUATIONS

2014 ◽  
Vol 19 (1) ◽  
pp. 118-126 ◽  
Author(s):  
Ahmet Bekir ◽  
Adem C. Cevikel ◽  
Ozkan Guner ◽  
Sait San
Keyword(s):  
Solitary Wave ◽  
Nonlinear Equations ◽  
Evolution Equations ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Bright Soliton ◽  
Physical Parameters ◽  
Kp Equation ◽  
Constant Coefficients

In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions and another wave ansatz in the form of tanhp function we obtain exact dark soliton solutions for these equations. The physical parameters in the soliton solutions are obtained nonlinear equations with constant coefficients.

scholarly journals The Basic (<i>G'/G</i>)-Expansion Method for the Fourth Order Boussinesq Equation

2012 ◽  
Vol 03 (10) ◽  
pp. 1144-1152 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Expansion Method

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.

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