Lie symmetry analysis for obtaining exact soliton solutions of generalized Camassa–Holm–Kadomtsev–Petviashvili equation

2020 ◽  
pp. 2150028
Author(s):  
Sachin Kumar ◽  
Monika Niwas ◽  
Ihsanullah Hamid
Keyword(s):  
Rational Function ◽  
Vector Fields ◽  
Soliton Solutions ◽  
Lie Symmetry ◽  
Trigonometric Function ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Nonlinear Odes ◽  
Petviashvili Equation ◽  
Exact Soliton Solutions

The prime objective of this paper is to obtain the exact soliton solutions by applying the two mathematical techniques, namely, Lie symmetry analysis and generalized exponential rational function (GERF) method to the (2+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petviashvili (g-CHKP) equation. First, we obtain Lie infinitesimals, possible vector fields, and commutative product of vectors for the g-CHKP equation. By the means of symmetry reductions, the g-CHKP equation reduced to various nonlinear ODEs. Subsequently, we implement the GERF method to the reduced ODEs with the help of computerized symbolic computation in Mathematica. Some abundant exact soliton solutions are obtained in the shapes of different dynamical structures of multiple-solitons like one-soliton, two-soliton, three-soliton, four-soliton, bell-shaped solitons, lump-type soliton, kink-type soliton, periodic solitary wave solutions, trigonometric function, hyperbolic trigonometric function, exponential function, and rational function solutions. Consequently, the dynamical structures of attained exact analytical solutions are discussed through 3D-plots via numerical simulation. A comparison with other results is also presented.

scholarly journals New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1001 ◽  
Author(s):  
Subhadarshan Sahoo ◽  
Santanu Saha Ray ◽  
Mohamed Aly Mohamed Abdou ◽  
Mustafa Inc ◽  
Yu-Ming Chu
Keyword(s):  
Conservation Laws ◽  
Fractional Differential Equations ◽  
Soliton Solutions ◽  
Logistic Function ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Fractional Differential ◽  
Physical Phenomena

New soliton solutions of fractional Jaulent-Miodek (JM) system are presented via symmetry analysis and fractional logistic function methods. Fractional Lie symmetry analysis is unified with symmetry analysis method. Conservation laws of the system are used to obtain new conserved vectors. Numerical simulations of the JM equations and efficiency of the methods are presented. These solutions might be imperative and significant for the explanation of some practical physical phenomena. The results show that present methods are powerful, competitive, reliable, and easy to implement for the nonlinear fractional differential equations.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham–Broer–Kaup–Like Equations

2017 ◽  
Vol 72 (3) ◽  
pp. 269-279 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Shou-Fu Tian ◽  
Chun-Yan Qin ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Vector Fields ◽  
Wave Equations ◽  
Boussinesq Equations ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
Bidirectional Propagation

AbstractIn this article, a generalised Whitham–Broer–Kaup–Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham–Broer–Kaup–Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

Symmetry reductions and exact solutions to the Sharma–Tasso–Olever equation

2016 ◽  
Vol 22 (2) ◽  
Author(s):  
Youwei Zhang
Keyword(s):  
Exact Solutions ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Powerful Technique ◽  
Symmetry Reductions

AbstractIn the present paper, the Sharma–Tasso–Olever (STO) equation is considered by the Lie symmetry analysis. All of the geometric vector fields to the STO equation are obtained, and then the symmetry reductions and exact solutions of the equation are investigated. Our results witness that symmetry analysis is a very efficient and powerful technique in finding the solutions of the proposed equation.

Symmetry analysis and invariant solutions of (3 + 1)-dimensional Kadomtsev–Petviashvili equation

2018 ◽  
Vol 15 (08) ◽  
pp. 1850125 ◽  
Author(s):  
Vishakha Jadaun ◽  
Sachin Kumar
Keyword(s):  
Lie Algebra ◽  
Zeta Functions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Lie Symmetry Method ◽  
Petviashvili Equation ◽  
Symmetry Method ◽  
Similarity Reductions

Based on Lie symmetry analysis, we study nonlinear waves in fluid mechanics with strong spatial dispersion. The similarity reductions and exact solutions are obtained based on the optimal system and power series method. We obtain the infinitesimal generators, commutator table of Lie algebra, symmetry group and similarity reductions for the [Formula: see text]-dimensional Kadomtsev–Petviashvili equation. For different Lie algebra, Lie symmetry method reduces Kadomtsev–Petviashvili equation into various ordinary differential equations (ODEs). Some of the solutions of [Formula: see text]-dimensional Kadomtsev–Petviashvili equation are of the forms — traveling waves, Weierstrass’s elliptic and Zeta functions and exponential functions.

Lie symmetry analysis, explicit solutions and conservation laws of the time fractional Clannish Random Walker’s Parabolic equation

2020 ◽  
pp. 2150074
Author(s):  
Panpan Wang ◽  
Wenrui Shan ◽  
Ying Wang ◽  
Qianqian Li
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Series Solutions ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction ◽  
Power Series Solutions ◽  
Conservation Theorem

In this paper, we mainly study the symmetry analysis and conservation laws of the time fractional Clannish Random Walker’s Parabolic (CRWP) equation. The vector fields and similarity reduction of the time fractional CRWP equation are obtained. In addition, based on the power series theory, a simple and effective approach for constructing explicit power series solutions is proposed. Finally, by use of the new conservation theorem, the conservation laws of the time fractional CRWP equation are constructed.

scholarly journals Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Huizhang Yang ◽  
Wei Liu ◽  
Yunmei Zhao
Keyword(s):  
Conservation Laws ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Bkp Equation

In this paper, the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili(BKP) equation is studied applying Lie symmetry analysis. We apply the Lie symmetry method to the (3 + 1)-dimensional generalized BKP equation and derive its symmetry reductions. Based on these symmetry reductions, some exact traveling wave solutions are obtained by using the tanh method and Kudryashov method. Finally, the conservation laws to the (3 + 1)-dimensional generalized BKP equation are presented by invoking the multiplier method.

scholarly journals Lie Symmetry Analysis and Exact Solutions of Generalized Fractional Zakharov-Kuznetsov Equations

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 601 ◽  
Author(s):  
Changzhao Li ◽  
Juan Zhang
Keyword(s):  
Exact Solutions ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
New Exact Solutions ◽  
Symmetry Properties

This paper considers the Lie symmetry analysis of a class of fractional Zakharov-Kuznetsov equations. We systematically show the procedure to obtain the Lie point symmetries for the equation. Accordingly, we study the vector fields of this equation. Meantime, the symmetry reductions of this equation are performed. Finally, by employing the obtained symmetry properties, we can get some new exact solutions to this fractional Zakharov-Kuznetsov equation.

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