scholarly journals Full Symmetry Groups and Exact Solutions to BKP and GKP Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Bo Ren ◽  
Jian-Yong Wang
Keyword(s):  
Exact Solutions ◽  
Symmetry Group ◽  
Symmetry Groups ◽  
Point Groups ◽  
Full Symmetry ◽  
The Relationship

We investigate the (2+1)-dimensional nonlinear BKP and GKP equations with the modified direct CK’s method. Then, we get its Lie point groups and the full symmetry group, and a relationship is constructed between the new solutions and the old one. Based on the relationship, the new solutions can be obtained by using a given solution of the equations.

Symmetry Reduction, Exact Solutions, and Conservation Laws of the (2+1)-Dimensional Dispersive Long Wave Equations

2009 ◽  
Vol 64 (9-10) ◽  
pp. 597-603 ◽  
Author(s):  
Zhong Zhou Dong ◽  
Yong Chen
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Symmetry Group ◽  
Infinite Number ◽  
Wave Equations ◽  
Direct Method ◽  
Discrete Groups ◽  
Point Symmetry Group ◽  
Long Wave ◽  
Full Symmetry

By means of the generalized direct method, we investigate the (2+1)-dimensional dispersive long wave equations. A relationship is constructed between the new solutions and the old ones and we obtain the full symmetry group of the (2+1)-dimensional dispersive long wave equations, which includes the Lie point symmetry group S and the discrete groups D. Some new forms of solutions are obtained by selecting the form of the arbitrary functions, based on their relationship. We also find an infinite number of conservation laws of the (2+1)-dimensional dispersive long wave equations.

scholarly journals Fundamental Domains for Rhombic Lattices with Dihedral Symmetry of Order 8

10.37236/7802 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Joseph Ray Clarence G. Damasco ◽  
Dirk Frettlöh ◽  
Manuel Joseph C. Loquias
Keyword(s):  
Symmetry Group ◽  
Fundamental Domain ◽  
Point Group ◽  
Symmetry Groups ◽  
Fundamental Domains ◽  
Open Case ◽  
Point Groups ◽  
Index 2 ◽  
Rhombic Lattice ◽  
Planar Lattices

We show by construction that every rhombic lattice $\Gamma$ in $\mathbb{R}^{2}$ has a fundamental domain whose symmetry group contains the point group of $\Gamma$ as a subgroup of index $2$. This solves the last open case of a question raised in a preprint by the authors on fundamental domains for planar lattices whose symmetry groups properly contain the point groups of the lattices.  

scholarly journals Влияние деформации на энергетический спектр и спектр оптического поглощения фуллерена C-=SUB=-20-=/SUB=- в модели Хаббарда

2019 ◽  
Vol 61 (2) ◽  
pp. 395
Author(s):  
А.В. Силантьев
Keyword(s):  
Group Theory ◽  
Hubbard Model ◽  
Symmetry Group ◽  
Energy Levels ◽  
Analytical Form ◽  
Symmetry Reduction ◽  
Energy Spectra ◽  
Symmetry Groups ◽  
Static Fluctuation Approximation ◽  
Static Fluctuation

Abstract —Anticommutator Green’s functions and energy spectra of fullerene C_20 with the I _ h , D _5 d , and D _3 d symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C_20 with the I _ h , D _5 d , and D _3 d symmetry groups have been determined. It is also shown how the energy levels of fullerene C_20 with the I _ h symmetry group are split with the symmetry reduction.

scholarly journals Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Masatomo Iwasa
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Singular Perturbation ◽  
Symmetry Group ◽  
Group Analysis ◽  
Lie Symmetry ◽  
Symmetry Groups ◽  
Lie Group Analysis ◽  
Constraint Equations ◽  
Perturbation Problems

Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior.

scholarly journals Structure Transformations in Broken Symmetry Groups—Abstraction and Visualization

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 440 ◽  
Author(s):  
Valery Rau ◽  
Igor Togunov ◽  
Tamara Rau ◽  
Sergey Polyakov
Keyword(s):  
Symmetry Group ◽  
Oriented Graph ◽  
Structure Study ◽  
Broken Symmetry ◽  
Transformation Groups ◽  
Evolutionary Trees ◽  
Symmetry Groups ◽  
Structure Development ◽  
Computer Visualization ◽  
Development Direction

The work reports the finding and the study of transformation groups with two conditional elements (binary transformations of abstract structures of the finite numerical sets with broken symmetry). The term Broken Symmetry Group (BSG) is introduced. Transformation examples of relevant structures are studied with computer visualization and application in real structure study. A special type of BSG was discovered, which describes the subsets of “evolutionary trees” with convergent and divergent properties of the oriented graph (orgraph) with structure-development direction edges and “growth spirals”.

scholarly journals Computing symmetry groups of polyhedra

2014 ◽  
Vol 17 (1) ◽  
pp. 565-581 ◽  
Author(s):  
David Bremner ◽  
Mathieu Dutour Sikirić ◽  
Dmitrii V. Pasechnik ◽  
Thomas Rehn ◽  
Achill Schürmann
Keyword(s):  
Linear Programming ◽  
Symmetry Group ◽  
Integer Linear Programming ◽  
Combinatorial Structure ◽  
Symmetry Groups ◽  
Graph Automorphism ◽  
Practical Experiences

AbstractKnowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial structure of a polyhedron. In each case we give algorithmic methods to compute the corresponding group and discuss some practical experiences. For practical purposes the linear symmetry group is the most important, as its computation can be directly translated into a graph automorphism problem. We indicate how to compute integral subgroups of the linear symmetry group that are used, for instance, in integer linear programming.

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