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On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory.
- Source :
-
Journal of Physics A: Mathematical & Theoretical . Feb2008, Vol. 41 Issue 6, p065205-065205. 1p. - Publication Year :
- 2008
-
Abstract
- Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper, we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of the application of the proposed procedure. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17518113
- Volume :
- 41
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Physics A: Mathematical & Theoretical
- Publication Type :
- Academic Journal
- Accession number :
- 44660520
- Full Text :
- https://doi.org/10.1088/1751-8113/41/6/065205