Kink, periodic, dark and bright soliton solutions of Kudryashov–Sinelshchikov equation using the improved tan$$\left( \frac{\phi (\eta )}{2}\right)$$-expansion technique

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.

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

Modern Physics Letters B ◽

10.1142/s0217984918500823 ◽

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.

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Solitary Wave Solution of Nonlinear PDEs Arising in Mathematical Physics

Open Physics ◽

10.1515/phys-2019-0043 ◽

2019 ◽

Vol 17 (1) ◽

pp. 381-389

Author(s):

Attia Rani ◽

Nawab Khan ◽

Kamran Ayub ◽

M. Yaqub Khan ◽

Qazi Mahmood-Ul-Hassan ◽

...

Keyword(s):

Solitary Wave ◽

Mathematical Models ◽

Solitary Wave Solution ◽

Nonlinear Differential Equations ◽

Soliton Solutions ◽

Nonlinear Pdes ◽

Wave Transformation ◽

Soliton Theory ◽

Nonlinear Mathematical Models ◽

Expansion Technique

Abstract The solution of nonlinear mathematical models has much importance and in soliton theory its worth has increased. In the present article, we have investigated the Caudrey-Dodd-Gibbon and Pochhammer-Chree equations, to discuss the physics of these equations and to attain soliton solutions. The exp(−ϕ(ζ ))-expansion technique is used to construct solitary wave solutions. A wave transformation is applied to convert the problem into the form of an ordinary differential equation. The drawn-out novel type outcomes play an essential role in the transportation of energy. It is noted that in the study, the approach is extremely reliable and it may be extended to further mathematical models signified mostly in nonlinear differential equations.

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

Mathematics ◽

10.3390/math8030341 ◽

2020 ◽

Vol 8 (3) ◽

pp. 341 ◽

Cited By ~ 9

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.

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Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

ITM Web of Conferences ◽

10.1051/itmconf/20182201056 ◽

2018 ◽

Vol 22 ◽

pp. 01056 ◽

Cited By ~ 1

Author(s):

Seyma Tuluce Demiray ◽

Hasan Bulut

Keyword(s):

Exact Solutions ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Soliton Solutions ◽

Nonlinear Evolution Equations ◽

Bright Soliton ◽

Generalized Kudryashov Method ◽

Kudryashov Method ◽

Ostrovsky Equation

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

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Bright Soliton Solutions in Degenerate Femi Gas near Feshbach Resonance

Chinese Physics Letters ◽

10.1088/0256-307x/26/12/120308 ◽

2009 ◽

Vol 26 (12) ◽

pp. 120308 ◽

Cited By ~ 8

Author(s):

Liu Hong ◽

He Dai-Hai ◽

Lou Sen-Yue ◽

He Xian-Tu

Keyword(s):

Feshbach Resonance ◽

Soliton Solutions ◽

Bright Soliton

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

International Journal of Modern Physics C ◽

10.1142/s0129183122500693 ◽

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.

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

Mathematical Modelling and Analysis ◽

10.3846/13926292.2014.893456 ◽

2014 ◽

Vol 19 (1) ◽

pp. 118-126 ◽

Cited By ~ 6

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.

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