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 Soliton solutions for (2+1) and (3+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony model equations and their applications

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 531-542 ◽  
Author(s):  
Kalim Tariq ◽  
Aly Seadawy
Keyword(s):  
Solitary Wave ◽  
Water Wave ◽  
Soliton Solutions ◽  
Fluid Flows ◽  
Wave Model ◽  
Wave Surface ◽  
Governing Equations ◽  
Ansatz Method ◽  
Solitary Wave Ansatz Method ◽  
Model Equations

The Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) model equations as a water wave model, are governing equations, for fluid flows, describes bidirectional propagating water wave surface. The soliton solutions for (2+1) and (3+1)-Dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equations have been extracted. The solitary wave ansatz method are adopted to approximate the solutions. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of the problem.

scholarly journals Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yarong Xia ◽  
Ruoxia Yao ◽  
Xiangpeng Xin
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Higher Order ◽  
Group Invariant ◽  
Residual Symmetry ◽  
Nonlinear Excitations ◽  
Group Invariant Solutions ◽  
Symmetry Transformations ◽  
Bidirectional Propagation ◽  
Truncated Painlevé Expansion

Under investigation in this paper is the higher-order Broer-Kaup(HBK) system, which describes the bidirectional propagation of long waves in shallow water. Via the standard truncated Painlevé expansion method, the residual symmetry of this system is derived. By introducing an appropriate auxiliary-dependent variable, the residual symmetry is successfully localized to Lie point symmetries. Via solving the initial value problems, the finite symmetry transformations are presented. However, the solution which obtained from the residual symmetry is a special group invariant solutions. In order to find more general solution of HBK system, we further generalize the residual symmetry method to the consistent tanh expansion (CTE) method and prove that the HBK system is CTE solvable, then the resonant soliton solutions and interaction solutions among different nonlinear excitations are obtained by the CET method.

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.

Multiple soliton, fusion, breather, lump, mixed kink-lump and periodic solutions to the extended shallow water wave model in (2+1)-dimensions

2020 ◽  
pp. 2150138
Author(s):  
Hajar F. Ismael ◽  
Aly Seadawy ◽  
Hasan Bulut
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Soliton Solutions ◽  
Quadratic Function ◽  
Wave Model ◽  
Simple Method ◽  
Shallow Water Wave ◽  
Hirota Bilinear Form ◽  
The One ◽  
Physical Phenomena

In this paper, we consider the shallow water wave model in the (2+1)-dimensions. The Hirota simple method is applied to construct the new dynamics one-, two-, three-, [Formula: see text]-soliton solutions, complex multi-soliton, fusion, and breather solutions. By using the quadratic function, the one-lump, mixed kink-lump and periodic lump solutions to the model are obtained. The Hirota bilinear form variable of this model is derived at first via logarithmic variable transform. The physical phenomena to this model are explored. The obtained results verify the proposed model.

scholarly journals New dark-bright soliton in the shallow water wave model

2020 ◽  
Vol 5 (4) ◽  
pp. 4027-4044 ◽  
Author(s):  
Gulnur Yel ◽  
◽  
Haci Mehmet Baskonus ◽  
Wei Gao ◽  
◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Model ◽  
Bright Soliton ◽  
Shallow Water Wave

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.

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.

Dark and bright soliton solutions and computational modeling of nonlinear regularized long wave model

2021 ◽  
Vol 104 (1) ◽  
pp. 661-682 ◽  
Author(s):  
Sanjay Kumar ◽  
Ram Jiwari ◽  
R. C. Mittal ◽  
Jan Awrejcewicz
Keyword(s):  
Computational Modeling ◽  
Soliton Solutions ◽  
Wave Model ◽  
Bright Soliton ◽  
Long Wave

scholarly journals New Lax Pairs and Darboux Transformation and Its Application to a Shallow Water Wave Model of Generalized KdV Type

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Huizhang Yang ◽  
Weiguo Rui
Keyword(s):  
Shallow Water ◽  
Spectral Problem ◽  
Darboux Transformation ◽  
Water Wave ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Wave Model ◽  
Lax Pairs ◽  
Shallow Water Wave ◽  
Generalized Kdv Equation

New Lax pairs of a shallow water wave model of generalized KdV equation type are presented. According to this Lax pair, we constructed a new spectral problem. By using this spectral problem, we constructed Darboux transformation with the help of a gauge transformation. Applying this Darboux transformation, some new exact solutions including double-soliton solution of the shallow water wave model of generalized KdV equation type are obtained. In order to visually show dynamical behaviors of these double soliton solutions, we plot graphs of profiles of them and discuss their dynamical properties.

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