New class of exact solutions of the Dirac equation

1975 ◽  
Vol 16 (10) ◽  
pp. 2089-2092 ◽  
Author(s):  
Franklin S. Felber ◽  
John H. Marburger
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
New Class

Exact solutions of Dirac equation

Pramana ◽  
1979 ◽  
Vol 12 (5) ◽  
pp. 475-480 ◽  
Author(s):  
S V Kulkarni ◽  
L K Sharma
Keyword(s):  
Dirac Equation ◽  
Exact Solutions

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

Exact solutions of Dirac equation on a static curved space–time

2019 ◽  
Vol 401 ◽  
pp. 21-39 ◽  
Author(s):  
M.D. de Oliveira ◽  
Alexandre G.M. Schmidt
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Space Time ◽  
Curved Space

A new class of exact solutions of the Vlasov equation

2001 ◽  
Vol 8 (12) ◽  
pp. 5081-5085 ◽  
Author(s):  
M. Y. Yu ◽  
Zhaoyang Chen ◽  
L. Stenflo
Keyword(s):  
Exact Solutions ◽  
Vlasov Equation ◽  
New Class

scholarly journals Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1867
Author(s):  
Alexander Breev ◽  
Alexander Shapovalov
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Homogeneous Space ◽  
Integration Method ◽  
Homogeneous Spaces ◽  
Separation Of Variables ◽  
General Structure ◽  
Three Dimensional ◽  
De Sitter ◽  
Elementary Functions

We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us to effectively apply the non-commutative integration method of linear partial differential equations on Lie groups. This method differs from the well-known method of separation of variables and to some extent can often supplement it. The general structure of the method developed is illustrated with an example of a homogeneous space which does not admit separation of variables in the Dirac equation. However, the basis of exact solutions to the Dirac equation is constructed explicitly by the non-commutative integration method. In addition, we construct a complete set of new exact solutions to the Dirac equation in the three-dimensional de Sitter space-time AdS3 using the method developed. The solutions obtained are found in terms of elementary functions, which is characteristic of the non-commutative integration method.

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