Lie symmetry analysis, optimal system, new solitary wave solutions and conservation laws of the Pavlov equation

2021 ◽  
Vol 94 ◽  
pp. 105560
Author(s):  
Nardjess Benoudina ◽  
Yi Zhang ◽  
Chaudry Masood Khalique
Keyword(s):  
Solitary Wave ◽  
Conservation Laws ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Solitary Wave Solutions ◽  
Lie Symmetry Analysis ◽  
Wave Solutions

scholarly journals Lie Symmetry Analysis and Dynamics of Exact Solutions of the (2+1)-Dimensional Nonlinear Sharma–Tasso–Olver Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Sachin Kumar ◽  
Ilyas Khan ◽  
Setu Rani ◽  
Behzad Ghanbari
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Main Concern ◽  
Solitary Wave Solutions ◽  
Lie Symmetry Analysis ◽  
Soliton Theory ◽  
Symmetry Reductions ◽  
Wave Solutions

In soliton theory, the dynamics of solitary wave solutions may play a crucial role in the fields of mathematical physics, plasma physics, biology, fluid dynamics, nonlinear optics, condensed matter physics, and many others. The main concern of this present article is to obtain symmetry reductions and some new explicit exact solutions of the (2 + 1)-dimensional Sharma–Tasso–Olver (STO) equation by using the Lie symmetry analysis method. The infinitesimals for the STO equation were achieved under the invariance criteria of Lie groups. Then, the two stages of symmetry reductions of the governing equation are obtained with the help of an optimal system. Meanwhile, this Lie symmetry method will reduce the STO equation into new partial differential equations (PDEs) which contain a lesser number of independent variables. Based on numerical simulation, the dynamical characteristics of the solitary wave solutions illustrate multiple-front wave profiles, solitary wave solutions, kink wave solitons, oscillating periodic solitons, and annihilation of parabolic wave structures via 3D plots.

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.

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 Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Expansion Method ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Similarity Reductions

Lie symmetry analysis is performed on a generalized two-dimensional nonlinear Kadomtsev-Petviashvili-modified equal width equation. The symmetries and adjoint representations for this equation are given and an optimal system of one-dimensional subalgebras is derived. The similarity reductions and exact solutions with the aid ofG′/G-expansion method are obtained based on the optimal systems of one-dimensional subalgebras. Finally conservation laws are constructed by using the multiplier method.

scholarly journals Lie symmetry analysis, conservation laws and analytical solutions for chiral nonlinear Schrödinger equation in (2 + 1)-dimensions

2020 ◽  
Vol 25 (3) ◽  
Author(s):  
Jin-Jin Mao ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang ◽  
Xing-Jie Yan
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Lie Symmetry ◽  
Nonlinear Schrodinger Equation ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
Nonlinear Schrödinger

In this work, we consider the chiral nonlinear Schrödinger equation in (2 + 1)-dimensions, which describes the envelope of amplitude in many physical media. We employ the Lie symmetry analysis method to study the vector field and the optimal system of the equation. The similarity reductions are analyzed by considering the optimal system. Furthermore, we find the power series solution of the equation with convergence analysis. Based on a new conservation law, we construct the conservation laws of the equation by using the resulting symmetries. 

Sign in / Sign up

Export Citation Format

Share Document