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.

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 On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
P. Masemola ◽  
A. H. Kara
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Schrodinger Equation ◽  
Lie Symmetries ◽  
Pt Symmetry ◽  
Noether Symmetries ◽  
Cubic Schrödinger Equation ◽  
The Relationship

An analysis of a PT symmetric coupler with “gain in one waveguide and loss in another” is made; a transformation in the PT system and some assumptions results in a scalar cubic Schrödinger equation. We investigate the relationship between the conservation laws and Lie symmetries and investigate a Lagrangian, corresponding Noether symmetries, conserved vectors, and exact solutions via “double reductions.”

Symmetries and conservation laws of a damped Boussinesq equation

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640012 ◽  
Author(s):  
María Luz Gandarias ◽  
María Rosa
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Source Term ◽  
Boussinesq Equation ◽  
Lie Symmetries ◽  
Multiplier Method ◽  
Independent Source ◽  
Damped Equation

In this work, we consider a damped equation with a time-independent source term. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. We also present some exact solutions. Conservation laws for this equation are constructed by using the multiplier method.

scholarly journals Nonlinear differential equations: Lie symmetries, conservation laws and other approaches of solving

2020 ◽  
Vol 13 (10) ◽  
pp. i-ii
Author(s):  
Chaudry Masood Khalique ◽  
◽  
Muhammad Usman ◽  
Maria Luz Gandarais ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Nonlinear Differential Equations ◽  
Lie Symmetries
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