scholarly journals Application of Lie Symmetry Analysis and Simplest Equation Method for Finding Exact Solutions of Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Hossein Jafari ◽  
Nematollah Kadkhoda ◽  
Chaudry Massod Khalique
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equations ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Equation Method ◽  
Lie Symmetry Analysis ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach

The Lie symmetry approach with simplest equation method is used to construct exact solutions of the bad Boussinesq and good Boussinesq equations. As the simplest equation, we have used the equation of Riccati.

scholarly journals Exact solutions and conservation laws of a coupled integrable dispersionless system

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 957-964 ◽  
Author(s):  
Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Applied Mathematics ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Equation Method ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
Simplest Equation Method ◽  
Mathematics And Physics

In this paper we study the coupled integrable dispersionless system (CIDS), which arises in the analysis of several problems in applied mathematics and physics. Lie symmetry analysis is performed on CIDS and symmetry reductions and exact solutions with the aid of simplest equation method are obtained. In addition, the conservation laws of the CIDS are also derived using the multiplier (and homotopy) approach.

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.

Symmetry analysis with similarity reduction, new exact solitary wave solutions and conservation laws of (3 + 1)-dimensional extended quantum Zakharov–Kuznetsov equation in quantum physics

2021 ◽  
pp. 2150163
Author(s):  
Vinita ◽  
S. Saha Ray
Keyword(s):  
Conservation Laws ◽  
Quantum Physics ◽  
Physical Structure ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Similarity Reduction ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach ◽  
Conservation Theorem

A recently defined (3+1)-dimensional extended quantum Zakharov–Kuznetsov (QZK) equation is examined here by using the Lie symmetry approach. The Lie symmetry analysis has been used to obtain the varieties in invariant solutions of the extended Zakharov–Kuznetsov equation. Due to existence of arbitrary functions and constants, these solutions provide a rich physical structure. In this paper, the Lie point symmetries, geometric vector field, commutative table, symmetry groups of Lie algebra have been derived by using the Lie symmetry approach. The simplest equation method has been presented for obtaining the exact solution of some reduced transform equations. Finally, by invoking the new conservation theorem developed by Nail H. Ibragimov, the conservation laws of QZK equation have been derived.

scholarly journals Symmetry properties and exact solutions of the time fractional Kolmogorov-Petrovskii-Piskunov equation

2019 ◽  
Vol 65 (5 Sept-Oct) ◽  
pp. 529 ◽  
Author(s):  
M. S. Hasheim ◽  
M. Inc ◽  
M. Bayram
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Conformable Fractional Derivative ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Symmetry Properties ◽  
Lie Symmetry Approach

In this paper, the time fractional Kolmogorov-Petrovskii-Piskunov (FKP) equation is analyzed by means of Lie symmetry approach. The FKP is reduced to ordinary differential equation of fractional order via the attained point symmetries. Moreover, the simplest equation method is used in construct the exact solutions of underlying equation with recently introduced conformable fractional derivative.

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