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.

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.

Bright soliton solutions, power series solutions and travelling wave solutions of a (3+1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (06) ◽  
pp. 1850082
Author(s):  
Ding Guo ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Bright Soliton ◽  
Travelling Wave Solutions ◽  
Series Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Power Series Solutions ◽  
De Vries

In this paper, we consider the (3[Formula: see text]+[Formula: see text]1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdV-KP) equation, which can be used to describe the nonlinear waves in plasma physics and fluid dynamics. By using solitary wave ansatz in the form of sech[Formula: see text] function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively. Moreover, we obtain its power series solutions with the convergence analysis. It is hoped that our results can provide the richer dynamical behavior of the KdV-type and KP-type equations.

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 Exact solutions of stochastic KdV equation with conformable derivatives in white noise environment

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 143-149
Author(s):  
Esma Ulutas ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
White Noise ◽  
Kdv Equation ◽  
Noise Analysis ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
White Noise Analysis ◽  
Wave Solutions ◽  
Conformable Derivatives

In this article, we have considered Wick-type stochastic Korteweg de Vries (KdV) equation with conformable derivatives. By the help of white noise analysis, Hermit transform and extended G?/G- expansion method, we have obtained exact travelling wave solutions of KdV equation with conformable derivatives. We have applied the inverse Hermit transform for stochastic soliton solutions and then we have shown how stochastic solutions can be presented as Brownian motion functional solutions by an application example.

scholarly journals Travelling Wave Solutions of the Schrödinger-Boussinesq System

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Adem Kılıcman ◽  
Reza Abazari
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Trigonometric Function ◽  
Boussinesq System ◽  
Hyperbolic Function ◽  
Travelling Wave Solutions ◽  
Physical Problems ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

We establish exact solutions for the Schrödinger-Boussinesq Systemiut+uxx−auv=0,vtt−vxx+vxxxx−b(|u|2)xx=0, whereaandbare real constants. The (G′/G)-expansion method is used to construct exact periodic and soliton solutions of this equation. Our work is motivated by the fact that the (G′/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. These solutions may be important and of significance for the explanation of some practical physical problems.

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 Construction of various soliton solutions via the simplified extended sinh-Gordon equation expansion method

2018 ◽  
Vol 22 ◽  
pp. 01062
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Hasan Bulut ◽  
Haci Mehmet Baskonus
Keyword(s):  
Gordon Equation ◽  
Quantum Hall ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Wave Transformation ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
2D And 3D

In this paper, we present the simplified version of the extended sinh-Gordon equation expansion method. The newly proposed approach is based on the well-known sinh-Gordon equation and a travelling wave transformation. We successfully employed this approach to the (2+1)-dimensional nonlinear Chiral Schrodinger's and various solitary wave solutions to the studied nonlinear model are successfully constructed. The (2+1)-dimensional nonlinear Chiral Schrodinger's equation describes the edge states of the fractional quantum hall effect. The 2D and 3D surfaces of some of the obtained solutions are plotted.

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

Sign in / Sign up

Export Citation Format

Share Document