scholarly journals Lie algebra classification, conservation laws and invariant solutions for modification of the generalization of the Emden--Fowler equation.

2021 ◽  
Author(s):  
Yeisson Acevedo Agudelo ◽  
Gabriel Loaiza Ossa ◽  
Oscar Londoño Duque ◽  
Danilo García Hernández
Keyword(s):  
Conservation Laws ◽  
Lie Algebra ◽  
Invariant Solutions ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Generating Operators ◽  
Variational Symmetries ◽  
The Given ◽  
Lie Algebra Classification ◽  
Fowler Equation

We obtain the optimal system’s generating operators associated to a modification of the generalization of the Emden–Fowler Equation. equation. Using those operators we characterize all invariant solutions associated to a generalized. Moreover, we present the variational symmetries and the corresponding conservation laws, using Noether’s theorem and Ibragimov’s method. Finally, we classify the Lie algebra associated to the given equation.

scholarly journals Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
G. Loaiza ◽  
Y. Acevedo ◽  
O.M.L. Duque ◽  
Danilo A. García Hernández
Keyword(s):  
Nonlinear Dynamics ◽  
Lie Algebra ◽  
Generalized Equation ◽  
Group Method ◽  
Invariant Solutions ◽  
Lie Group Method ◽  
Points Of View ◽  
Generating Operators ◽  
The Given ◽  
Lie Algebra Classification

We obtain the optimal system’s generating operators associated with a generalized Levinson–Smith equation; this one is related to the Liénard equation which is important for physical, mathematical, and engineering points of view. The underlying equation has applications in mechanics and nonlinear dynamics as well. This equation has been widely studied in the qualitative scheme. Here, we treat the equation by using the Lie group method, and we obtain certain operators; using those operators, we characterized all invariants solutions associated with the generalized equation of Levinson Smith considered in this paper. Finally, we classify the Lie algebra associated with the given equation.

Introduction

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Conservation Laws ◽  
Lagrangian Mechanics ◽  
General Introduction ◽  
Noether’S Theorem ◽  
Noether's Theorem

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is included.

scholarly journals Conservation Laws in Physics – Emmy Noether’s Theorem

2014 ◽  
Vol 29 ◽  
pp. 55-61
Author(s):  
Daniela Manolea
Keyword(s):  
Conservation Laws ◽  
Celestial Body ◽  
Practical Importance ◽  
Microscopic Level ◽  
Human Knowledge ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
The World ◽  
Physical Laws ◽  
Practical Impact

The study is explanatory-interpretative and argues the practical character of Physics. It starts from premise that formation of a correct conception of the world begins with the understanding of physics. It is one of the earliest chapters of human knowledge, studying the material world from the microscopic level of the particles to the macroscopic level of the celestial body. As an example for the practical importance of applying the laws of physics take the set of physical laws of conservation, in particular, it explains the practical impact of Emmy Noether's Theorem.

On symmetries and conservation laws of some spacetimes in f(R, T) gravity

2019 ◽  
Vol 34 (36) ◽  
pp. 1975003
Author(s):  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
B. Gadjagboui
Keyword(s):  
Conservation Laws ◽  
Detailed Analysis ◽  
Bianchi Type ◽  
Type I ◽  
Noether’S Theorem ◽  
Bianchi Type I ◽  
Plane Symmetric ◽  
Locally Rotationally Symmetric ◽  
Rotationally Symmetric ◽  
Variational Symmetries

We undertake a detailed analysis of the symmetry structures of the plane symmetric and the locally rotationally symmetric (LRS) Bianchi type I spacetimes in the [Formula: see text] gravity. In particular, we construct all the variational symmetries associated with its Lagrangian and, in some cases, construct the associated conservation laws using Noether’s theorem. Giving a comparison between isometries and variational symmetries, we give symmetry structures of some well-known spacetimes.

scholarly journals About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof

2019 ◽  
Vol 22 (4) ◽  
pp. 871-898 ◽  
Author(s):  
Jacky Cresson ◽  
Anna Szafrańska
Keyword(s):  
Local Group ◽  
Type Theorem ◽  
Classical Case ◽  
Alternative Proof ◽  
Lagrangian Systems ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Definition Of ◽  
Variational Symmetries ◽  
Discrete Setting

Abstract Recently, the fractional Noether’s theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether’s type Theorem, in particular ([9], Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis of the proof proposed by G. Frederico and D.F.M. Torres in [9] which is based on a fractional generalization of a method proposed by J. Jost and X.Li-Jost in the classical case. This method is also used in [10]. We first detail this method and then its fractional version. Several points leading to difficulties are put in evidence, in particular the definition of variational symmetries and some properties of local group of transformations in the fractional case. These difficulties arise in several generalization of the Jost’s method, in particular in the discrete setting. We then derive a fractional Noether’s Theorem following this strategy, correcting the initial statement of Frederico and Torres in [9] and obtaining an alternative proof of the main result of Atanackovic and al. [3].

Conservation laws of linear elasticity in stress formulations

2005 ◽  
Vol 461 (2053) ◽  
pp. 99-116 ◽  
Author(s):  
Shaofan Li ◽  
Anurag Gupta ◽  
Xanthippi Markenscoff
Keyword(s):  
Conservation Laws ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Cauchy Stress ◽  
General Boundary Conditions ◽  
Cauchy Stress Tensor ◽  
Equilibrium Equations ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Three Dimensional Elasticity

In this paper, we present new conservation laws of linear elasticity which have been discovered. These newly discovered conservation laws are expressed solely in terms of the Cauchy stress tensor, and they are genuine, non–trivial conservation laws that are intrinsically different from the displacement conservation laws previously known. They represent the variational symmetry conditions of combined Beltrami–Michell compatibility equations and the equilibrium equations. To derive these conservation laws, Noether's theorem is extended to partial differential equations of a tensorial field with general boundary conditions. By applying the tensorial version of Noether's theorem to Pobedrja's stress formulation of three–dimensional elasticity, a class of new conservation laws in terms of stresses has been obtained.

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