scholarly journals Approximate Lie symmetries and approximate invariants of the orbit differential equation for perturbed Kepler system

2010 ◽  
Vol 59 (10) ◽  
pp. 6764
Author(s):  
Lou Zhi-Mei
Keyword(s):  
Differential Equation ◽  
Lie Symmetries ◽  
Kepler System ◽  
Approximate Lie Symmetries

Lie symmetries analysis and conservation laws for the fractional Calogero–Degasperis–Ibragimov–Shabat equation

2018 ◽  
Vol 15 (07) ◽  
pp. 1850110 ◽  
Author(s):  
S. Sahoo ◽  
S. Saha Ray
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Operator ◽  
Conservation Laws ◽  
Symmetry Analysis ◽  
Lie Symmetries ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Conservation Theorem

The present paper includes the study of symmetry analysis and conservation laws of the time-fractional Calogero–Degasperis–Ibragimov–Shabat (CDIS) equation. The Erdélyi–Kober fractional differential operator has been used here for reduction of time fractional CDIS equation into fractional ordinary differential equation. Also, the new conservation theorem has been used for the analysis of the conservation laws. Furthermore, the new conserved vectors have been constructed for time fractional CDIS equation by means of the new conservation theorem with formal Lagrangian.

Energy of the Kerr–Newman-AdS black hole by using approximate Lie symmetries

2010 ◽  
Vol 43 (4) ◽  
pp. 1037-1045 ◽  
Author(s):  
Ibrar Hussain
Keyword(s):  
Black Hole ◽  
Lie Symmetries ◽  
Approximate Lie Symmetries

scholarly journals A Forgotten Differential Equation Studied by Jacopo Riccati Revisited in Terms of Lie Symmetries

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1312
Author(s):  
Daniele Ritelli
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Hypergeometric Functions ◽  
Solution Method ◽  
Complete Solution ◽  
Lie Symmetries ◽  
Parameter Family ◽  
Original Solution ◽  
The One ◽  
Two Parameter

In this paper we present a two parameter family of differential equations treated by Jacopo Riccati, which does not appear in any modern repertoires and we extend the original solution method to a four parameter family of equations, translating the Riccati approach in terms of Lie symmetries. To get the complete solution, hypergeometric functions come into play, which, of course, were unknown in Riccati’s time. Re-discovering the method introduced by Riccati, called by himself dimidiata separazione (splitted separation), we arrive at the closed form integration of a differential equation, more general to the one treated in Riccati’s contribution, and which also does not appear in the known repertoires.

scholarly journals Lie symmetries and Noether symmetries

2012 ◽  
Vol 6 (2) ◽  
pp. 238-246 ◽  
Author(s):  
P.G.L. Leach
Keyword(s):  
Differential Equation ◽  
First Integral ◽  
Lie Symmetries ◽  
Noether Symmetries

We demonstrate that so-called nonnoetherian symmetries with which a known first integral is associated of a differential equation derived from a Lagrangian are in fact noetherian. The source of the misunderstanding lies in the nonuniqueness of the Lagrangian.

scholarly journals A consistent approach to approximate Lie symmetries of differential equations

2017 ◽  
Vol 91 (1) ◽  
pp. 371-386 ◽  
Author(s):  
Rosa Di Salvo ◽  
Matteo Gorgone ◽  
Francesco Oliveri
Keyword(s):  
Differential Equations ◽  
Lie Symmetries ◽  
Symmetries Of Differential Equations ◽  
Approximate Lie Symmetries ◽  
Consistent Approach
Sign in / Sign up

Export Citation Format

Share Document