Lie subgroups of the symmetry group of the equations describing a nonstationary and isentropic flow: Invariant and partially invariant solutions

1994 ◽  
Vol 72 (7-8) ◽  
pp. 362-374 ◽  
Author(s):  
A. M. Grundland ◽  
L. Lalague
Keyword(s):  
Symmetry Group ◽  
Dimensional Space ◽  
Projective Group ◽  
Invariant Solutions ◽  
Partially Invariant Solutions ◽  
Isentropic Flow ◽  
Dimensional Space Time ◽  
Group A ◽  
Special Case

We study the symmetries of the equations describing a nonstationary and isentropic flow for an ideal and compressible fluid in four-dimensional space-time. We prove that this system of equations is invariant under the Galilean-similitude group. In the special case of the adiabatic exponent γ = 5/3, corresponding to a diatomic gas, the symmetry group of this system is larger. It is invariant under the Galilean-projective group. A representatives list of subalgebras of Galilean similitude and Galilean-projective Lie algebras, obtained by the method of classification by conjugacy classes under the action of their respective Lie groups, is presented. The results are given in a normalized list and summarized in tables. Examples of invariant and nonreducible partially invariant solutions, obtained from this classification, is constructed. The final part of this work contains an analysis of this classification in connection with a further classification of the symmetry algebras for the Euler and magnetohydrodynamics equations.

A differential constraints approach to partial invariance

1995 ◽  
Vol 6 (6) ◽  
pp. 631-637 ◽  
Author(s):  
Jeffrey Ondich
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Invariant Solutions ◽  
Differential Constraints ◽  
Partially Invariant Solutions ◽  
Prandtl Equations ◽  
Partial Invariance ◽  
Special Case ◽  
Method Of Differential Constraints

Ovsiannikov's method of partially invariant solutions of differential equations can be considered to be a special case of the method of differential constraints introduced by Yanenko and by Olver and Rosenau. Differential constraints are used to construct non-reducible partially invariant solutions of the boundary layer or Prandtl equations.

scholarly journals Adinkra (in)equivalence from Coxeter group representations: A case study

2014 ◽  
Vol 29 (06) ◽  
pp. 1450029 ◽  
Author(s):  
Isaac Chappell ◽  
S. James Gates ◽  
T. Hübsch
Keyword(s):  
Dimensional Space ◽  
Solution Space ◽  
Group Representations ◽  
Dimensional Solution ◽  
Signed Permutation ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Definition Of

Using a Mathematica TM code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4×4 matrices, which in sets of four, provide representations of the 𝒢ℛ(4, 4) algebra, closely related to the 𝒩 = 1 (simple) supersymmetry algebra in four-dimensional space–time. Following after ideas discussed in previous papers about automorphisms and classification of adinkras and corresponding supermultiplets, we make a new and alternative proposal to use equivalence classes of the (unsigned) permutation group S4 to define distinct representations of higher-dimensional spin bundles within the context of adinkras. For this purpose, the definition of a dual operator akin to the well-known Hodge star is found to partition the space of these 𝒢ℛ(4, 4) representations into three suggestive classes.

scholarly journals Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie

2021 ◽  
Vol 39 (2) ◽  
Author(s):  
Danilo García Hernández ◽  
Oscar Mario Londoño Duque ◽  
Yeisson Acevedo ◽  
Gabriel Loaiza
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Complete Classification ◽  
Lie Symmetry ◽  
Invariant Solutions ◽  
Generating Operators ◽  
Alternative Solutions ◽  
Schwarz Equation

We obtain the complete classification of the Lie symmetry group and the optimal system’s generating operators associated with a particular case of the generalized Kummer - Schwarz equation. Using those operators we characterize all invariant solutions, alternative solutions were found for the equation studied and the Lie algebra associated with the symmetry group is classified.

scholarly journals COLLAPSING SHELLS OF RADIATION IN HIGHER DIMENSIONAL SPACE–TIME AND COSMIC CENSORSHIP CONJECTURE

2001 ◽  
Vol 16 (27) ◽  
pp. 4481-4488 ◽  
Author(s):  
S. G. GHOSH ◽  
R. V. SARAYKAR ◽  
A. BEESHAM
Keyword(s):  
Dimensional Space ◽  
Cosmic Censorship ◽  
Space Time ◽  
Naked Singularities ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Self Similar ◽  
Strong Curvature ◽  
Special Case ◽  
Cosmic Censorship Conjecture

Gravitational collapse of radiation shells in a non-self-similar higher dimensional spherically symmetric space–time is studied. Strong curvature naked singularities form a highly inhomogeneous collapse, violating the cosmic censorship conjecture. As a special case, self similar models can be constructed.

scholarly journals Soliton Molecules and Full Symmetry Groups to the KdV-Sawada-Kotera-Ramani Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Na Xiong ◽  
Ya-Xuan Yu ◽  
Biao Li
Keyword(s):  
Symmetry Group ◽  
Direct Method ◽  
Dimensional Space ◽  
Invariant Solution ◽  
Soliton Solutions ◽  
General Group ◽  
One Dimensional ◽  
Group Invariant ◽  
Group A ◽  
Full Symmetry

By N -soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate the resonances of solitons in one-dimensional space. An asymmetric soliton can be formed by adjusting the distance between two solitons of soliton molecule to small enough. The interactions among multiple soliton molecules for the equation are elastic. Then, full symmetry group is derived for the KSKR equation by the symmetry group direct method. From the full symmetry group, a general group invariant solution can be obtained from a known solution.

scholarly journals CLASSIFICATION OF STANDARD MODEL PARTICLES IN E6 ORBIFOLD GRAND UNIFIED THEORIES

2013 ◽  
Vol 28 (14) ◽  
pp. 1350055 ◽  
Author(s):  
YOSHIHARU KAWAMURA ◽  
TAKASHI MIURA
Keyword(s):  
Standard Model ◽  
Dimensional Space ◽  
Space Time ◽  
Text Representation ◽  
Zero Modes ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Dimensional Space Time

We classify the standard model fermions, which originate from bulk fields of the 27 or [Formula: see text] representation after orbifold breaking, in E6 grand unified theories on five- or six-dimensional space–time, under the condition that q, ec and uc survive as zero modes for each 27 or [Formula: see text]. We study features of supersymmetric SU(5) ×U(1)1 ×U(1)2 model.

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