Symmetry and conservation law structures of some anti-self-dual (ASD) manifolds

Pramana ◽  
2016 ◽  
Vol 87 (5) ◽  
Author(s):  
J BASINGWA ◽  
A H KARA ◽  
ASHFAQUE H BOKHARI ◽  
R A MOUSA ◽  
F D ZAMAN
Keyword(s):  
Conservation Law ◽  
Symmetry And Conservation Law

On the symmetry and conservation law classification of the de Sitter–Schwarzschild metric and the corresponding wave and Klein–Gordon equations

2020 ◽  
Vol 17 (11) ◽  
pp. 2050172
Author(s):  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
F. D. Zaman ◽  
B. B. I. Gadjagboui
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
De Sitter ◽  
Killing Vectors ◽  
Schwarzschild Geometry ◽  
Klein Gordon ◽  
Spacetime Metric ◽  
Variational Symmetries ◽  
Symmetry And Conservation Law

The main purpose of this work is to focus on a discussion of Lie symmetries admitted by de Sitter–Schwarzschild spacetime metric, and the corresponding wave or Klein–Gordon equations constructed in the de Sitter–Schwarzschild geometry. The obtained symmetries are classified and the variational (Noether) conservation laws associated with these symmetries via the natural Lagrangians are obtained. In the case of the metric, we obtain additional variational ones when compared with the Killing vectors leading to additional conservation laws and for the wave and Klein–Gordon equations, the variational symmetries involve less tedious calculations as far as invariance studies are concerned.

scholarly journals Symmetries, pseudosymmetries and conservation laws in Lagrangian and Hamiltonian k-symplectic formalisms

2016 ◽  
Vol 13 (03) ◽  
pp. 1650026
Author(s):  
Florian Munteanu
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Systems ◽  
Conservation Law ◽  
Type Theorem ◽  
Natural Extension ◽  
Lagrangian Systems ◽  
Symmetry And Conservation Law

In this paper, we will present Lagrangian and Hamiltonian [Formula: see text]-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for [Formula: see text]-symplectic Hamiltonian systems and [Formula: see text]-symplectic Lagrangian systems.

SYMMETRY AND CONSERVATION LAW CLASSIFICATION AND EXACT SOLUTIONS TO THE GENERALIZED KdV TYPES OF EQUATIONS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250188 ◽  
Author(s):  
HANZE LIU ◽  
JIBIN LI ◽  
LEI LIU
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Conservation Law ◽  
Vector Fields ◽  
Nonlinear Partial Differential Equations ◽  
Second Order ◽  
Analytic Method ◽  
Composite Function ◽  
Symmetry And Conservation Law

In this paper, complete geometric symmetry and conservation law classification of the generalized KdV types of equations are investigated. All of the geometric vector fields and second-order multipliers for the equations are obtained, and the corresponding conservation laws of the equations are presented explicitly. These comprise all of the second-order conservation laws for the equations. Furthermore, an analytic method is developed for dealing with the exact solutions to the generalized nonlinear partial differential equations with composite function terms.

A solution of the conservation law form of the Serre equations

2016 ◽  
Vol 57 ◽  
pp. 385
Author(s):  
Christopher Zoppou ◽  
Stephen Roberts ◽  
Jason Pitt
Keyword(s):  
Conservation Law

scholarly journals The zilch electromagnetic conservation law revisited

2020 ◽  
Vol 61 (12) ◽  
pp. 122902
Author(s):  
Sajad Aghapour ◽  
Lars Andersson ◽  
Kjell Rosquist
Keyword(s):  
Conservation Law

scholarly journals The magnetic helicity density patterns from non-axisymmetric solar dynamo

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Valery V. Pipin
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Conservation Law ◽  
Large Scale ◽  
Solar Dynamo ◽  
Magnetic Helicity ◽  
Dynamo Model ◽  
Density Distributions ◽  
Large Scale Magnetic Field ◽  
Helicity Conservation

We study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density patterns around the bipolar regions depend on the configuration of the ambient large-scale magnetic field, and in general they show a quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time–latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions shows two bands of sign for the density distributions in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to surface differential rotation.

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