Symmetry analysis of differential equations: a primer

2018 ◽  
Author(s):  
Eric Jason Albright ◽  
James D. McHardy ◽  
Scott D. Ramsey ◽  
Joseph H. Schmidt
Keyword(s):  
Differential Equations ◽  
Symmetry Analysis

scholarly journals Symbolic Implementation of Preliminary Group Classiffication for Ordinary Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
K. S. Govinder
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Group Classification ◽  
Symmetry Analysis ◽  
Analysis Package ◽  
Small File ◽  
Fowler Equation ◽  
Preliminary Group

We apply the method of preliminary group classification to ordinary differential equations of the formy(n)=E(x,y,y',…,y(n-1),fi(x)),  i=0,…,m.We show how this method can be implemented via the popular symmetry analysis packagePROGRAM LIEprovided that the package is supplemented with a small file. We then apply this method to an extension of the generalised Emden-Fowler equation given byy′′=∑i=25fixyi.

scholarly journals Conservation laws and exact solutions for the generalized Ostrovsky equation using symmetry analysis

2021 ◽  
Author(s):  
Sol Sáez
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Symmetry Analysis ◽  
Partial Differential ◽  
Wide Range ◽  
Depth Study ◽  
Ostrovsky Equation

In this work we consider a generalized Ostrovsky equation depending on two arbitrary functions and we make an in-depth study of this equation. We obtain the Lie symmetries which are admitted by this equation and some exact solutions as a periodic or solitary waves, obtained through ordinary and partial differential equations. Also, by means of the concept of multiplier, we obtain a wide range of conservation laws which preserve properties of the generalized Ostrovsky equation.

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