Approximate symmetries and conservation laws of the geodesic equations for the Schwarzschild metric

2007 ◽  
Vol 51 (1-2) ◽  
pp. 183-188 ◽  
Author(s):  
A. H. Kara ◽  
F. M. Mahomed ◽  
Asghar Qadir
Keyword(s):  
Conservation Laws ◽  
Approximate Symmetries ◽  
Schwarzschild Metric ◽  
Geodesic Equations

scholarly journals Approximate symmetries and similarity solutions for wave equations on liquid films

2020 ◽  
pp. 18-18
Author(s):  
Sameerah Jamal ◽  
Andronikos Paliathanasis
Keyword(s):  
Conservation Laws ◽  
Small Amplitude ◽  
Wave Equations ◽  
Liquid Films ◽  
Similarity Solutions ◽  
Lie Symmetries ◽  
Long Waves ◽  
Approximate Symmetries ◽  
Approximate Similarity ◽  
Perturbation Parameters

We study the exact and approximate Lie symmetries for two equations which describe long waves with small amplitude on liquid films. Specifically, we study the 1+2 Benney-Luke and the 1+1 Benney-Lin equations, both from an exact and approximate perspective. To induce approximate symmetries, we show that terms involving derivatives higher than two are necessarily selected as the perturbation parameters. We construct conservation laws for both equations, and illustrate how the approximate point symmetries can be used to determine approximate similarity solutions.

scholarly journals Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Tahir Ayaz ◽  
Farhad Ali ◽  
Wali Khan Mashwani ◽  
Israr Ali Khan ◽  
Zabidin Salleh ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Order Differential Equation ◽  
Kdv Equation ◽  
Third Order ◽  
Lagrange Method ◽  
Approximate Symmetries ◽  
Weakly Nonlinear ◽  
The Kdv Equation ◽  
De Vries ◽  
Perturbed Kdv Equation

The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for different classes of the perturbed function. Partial Lagrange method is used to obtain the approximate symmetries and their corresponding conservation laws of the KdV equation. The purpose of this study is to find particular perturbation (function) for which the number of approximate symmetries of perturbed KdV equation is greater than the number of symmetries of KdV equation so that explore something hidden in the system.

Particles dynamics around time conformal quintessential Schwarzschild black hole

2020 ◽  
Vol 29 (13) ◽  
pp. 2050095
Author(s):  
Israr Ali Khan ◽  
Amir Sultan Khan ◽  
Saeed Islam ◽  
Farhad Ali
Keyword(s):  
Black Hole ◽  
Small Parameter ◽  
Conservation Laws ◽  
Charged Particles ◽  
Conformal Factor ◽  
Noether Symmetries ◽  
Schwarzschild Black Hole ◽  
Approximate Symmetries ◽  
Particles Dynamics ◽  
General Time

In this paper, the effect of time is explored on the dynamics of neutral and charged particles around the Schwarzschild (Sch) black hole (BH) environed by quintessence. We introduce a general time conformal factor [Formula: see text] to the quintessential Sch spacetime, where [Formula: see text] is a time ([Formula: see text])-dependent function and [Formula: see text], a small parameter, that causes perturbation in the corresponding spacetime. The Noether symmetry equation is obtained with the help of Lagrangian corresponding to time conformal Sch spacetime environed by quintessence. Consequently, we get a 19 partial differential equations (PDEs) system. The solution of this system gives Noether symmetries, Noether approximate symmetries, and the corresponding conservation laws. The dynamics of neutral/charged particles are studied as well as graphically analyzed at the foot of these invariants.

scholarly journals Approximate Symmetry Analysis and Approximate Conservation Laws of Perturbed KdV Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yu-Shan Bai ◽  
Qi Zhang
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Symmetry Algebra ◽  
Optimal System ◽  
Approximate Symmetry ◽  
Invariant Solutions ◽  
Approximate Symmetries ◽  
One Dimensional ◽  
Perturbed Kdv Equation ◽  
Partial Lagrangian

Approximate symmetries, which are admitted by the perturbed KdV equation, are obtained. The optimal system of one-dimensional subalgebra of symmetry algebra is obtained. The approximate invariants of the presented approximate symmetries and some new approximately invariant solutions to the equation are constructed. Moreover, the conservation laws have been constructed by using partial Lagrangian method.

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