Hidden Symmetries: Lie Groups and Economic Conservation Laws

1984 ◽  
pp. 35-54
Author(s):  
Ryuzo Sato ◽  
Takayuki Nôno ◽  
Fumitake Mimura
Keyword(s):  
Conservation Laws ◽  
Lie Groups ◽  
Hidden Symmetries

scholarly journals Group analysis and variational principle for nonlinear (3+1) schrodinger equation

2010 ◽  
Vol 7 (1) ◽  
pp. 115-122
Author(s):  
Eman Salem A. Alaidarous
Keyword(s):  
Variational Principle ◽  
Schrödinger Equation ◽  
Conservation Laws ◽  
Lie Groups ◽  
Schrodinger Equation ◽  
Group Analysis ◽  
Lie Symmetry ◽  
Functional Integral ◽  
Symmetry Groups ◽  
Conserved Currents

The generators of the admitted variational Lie symmetry groups are derived and conservation laws for the conserved currents are obtained via Noether's theorem. Moreover, the consistency of a functional integral are derived for the nonlinear Schrödinger equation. In addition to this analysis functional integral are studied using Lie groups.

scholarly journals Addendum: Hidden symmetries, trivial conservation laws and Casimir invariants in geophysical fluid dynamics (2018 J. Phys. Commun. 2 115018)

2021 ◽  
Vol 5 (11) ◽  
pp. 119401
Author(s):  
Martin Charron ◽  
Ayrton Zadra
Keyword(s):  
Fluid Dynamics ◽  
Conservation Laws ◽  
Arbitrary Function ◽  
Conservation Law ◽  
Hamiltonian Formulation ◽  
Internal Symmetry ◽  
Geophysical Fluid Dynamics ◽  
Hidden Symmetries ◽  
Casimir Invariants ◽  
Symmetry Transformations

Abstract An extension is proposed to the internal symmetry transformations associated with mass, entropy and other Clebsch-related conservation in geophysical fluid dynamics. Those symmetry transformations were previously parameterized with an arbitrary function  of materially conserved Clebsch potentials. The extension consists in adding potential vorticity q to the list of fields on which a new arbitrary function  depends. If  = q  ( s ) , where  ( s ) is an arbitrary function of specific entropy s, then the symmetry is trivial and gives rise to a trivial conservation law. Otherwise, the symmetry is non-trivial and an associated non-trivial conservation law exists. Moreover, the notions of trivial and non-trivial Casimir invariants are defined. All non-trivial symmetries that become hidden following a reduction of phase space are associated with non-trivial Casimir invariants of a non-canonical Hamiltonian formulation for fluids, while all trivial conservation laws are associated with trivial Casimir invariants.

scholarly journals Conservation Laws and Exact Solutions for a Reaction-Diffusion Equation with a Variable Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhijie Cao ◽  
Yiping Lin
Keyword(s):  
Diffusion Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Groups ◽  
Variable Coefficient ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation

In this paper a variable-coefficient reaction-diffusion equation is studied. We classify the equation into three kinds by different restraints imposed on the variable coefficientb(x)in the process of solving the determining equations of Lie groups. Then, for each kind, the conservation laws corresponding to the symmetries obtained are considered. Finally, some exact solutions are constructed.

scholarly journals PSEUDODUALITY AND CONSERVED CURRENTS IN SIGMA MODELS

2009 ◽  
Vol 24 (02) ◽  
pp. 123-134 ◽  
Author(s):  
MUSTAFA SARISAMAN
Keyword(s):  
Conservation Laws ◽  
Sigma Models ◽  
Lie Groups ◽  
Infinite Number ◽  
Two Dimensions ◽  
Compact Lie Groups ◽  
Current Conservation ◽  
Conserved Currents

We discuss the current conservation laws in sigma models based on a compact Lie groups of the same dimensionality and connected to each other via pseudoduality transformations in two dimensions. We show that pseudoduality transformations induce an infinite number of nonlocal conserved currents on the pseudodual manifold.

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

1995 ◽  
Author(s):  
Josi A. de Azcárraga ◽  
Josi M. Izquierdo
Keyword(s):  
Lie Groups ◽  
Lie Algebras
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