Solitary wave solutions of (3+1)-dimensional extended Zakharov–Kuznetsov equation by Lie symmetry approach

2019 ◽  
Vol 77 (8) ◽  
pp. 2096-2113 ◽  
Author(s):  
Sachin Kumar ◽  
Dharmendra Kumar
Keyword(s):  
Solitary Wave ◽  
Lie Symmetry ◽  
Solitary Wave Solutions ◽  
Symmetry Approach ◽  
Wave Solutions ◽  
Lie Symmetry Approach

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.

scholarly journals Exact Solutions ofϕ4Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Hossein Jafari ◽  
Nematollah Kadkhoda ◽  
Chaudry Masood Khalique
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Travelling Wave ◽  
Lie Symmetry ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Symmetry Approach ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach

This paper obtains the exact solutions of theϕ4equation. The Lie symmetry approach along with the simplest equation method and the Exp-function method are used to obtain these solutions. As a simplest equation we have used the equation of Riccati in the simplest equation method. Exact solutions obtained are travelling wave solutions.

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