scholarly journals Lie Symmetries of Differential Equations by Computer Algebra

1996 ◽  
Vol 1 (1) ◽  
pp. 15-20
Author(s):  
Mehmet Can
Keyword(s):  
Differential Equations ◽  
Computer Algebra ◽  
Lie Symmetries ◽  
Symmetries Of Differential Equations

scholarly journals Charged radiating stars with Lie symmetries

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
G. Z. Abebe ◽  
S. D. Maharaj
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Equations Of State ◽  
Lie Symmetries ◽  
Boundary Equation ◽  
Symmetries Of Differential Equations ◽  
Radiating Stars ◽  
Barotropic Equation ◽  
Radiating Star ◽  
General Relativistic

Abstract We consider the general model of an accelerating, expanding and shearing radiating star in the presence of charge. Using a new set of variables arising from the Lie symmetries of differential equations we transform the boundary equation into ordinary differential equations. We present several new exact models for a charged gravitating sphere. A particular family of solution may be interpreted as a generalised Euclidean star in the presence of the electromagnetic field. This family admits a linear barotropic equation of state. In the uncharged limit, we regain general relativistic stellar models where proper and areal radii are equal, and its generalisations. Our group theoretical approach selects the physically important cases of Euclidean stars and equations of state.

scholarly journals Approximate Noether Symmetries of Perturbed Lagrangians and Approximate Conservation Laws

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2900
Author(s):  
Matteo Gorgone ◽  
Francesco Oliveri
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Variational Problems ◽  
Lie Symmetries ◽  
Noether Symmetries ◽  
Noether Theorem ◽  
Symmetries Of Differential Equations ◽  
Approximate Lie Symmetries ◽  
Consistent Approach

In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we state an approximate Noether theorem leading to the construction of approximate conservation laws. Some illustrative applications are presented.

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