A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere
Certain algebraic solutions of the Klein-Gordon equation which involve Bessel functions are examined. It is demonstrated that these functions constitute an infinite series, each term of which is the solution of a boundary value problem involving a combination of source functions which comprise delta...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
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| Series: | Annales Geophysicae |
| Online Access: | http://www.ann-geophys.net/12/220/1994/angeo-12-220-1994.html |
| _version_ | 1811298694984630272 |
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| author | T. R. Robinson |
| author_facet | T. R. Robinson |
| author_sort | T. R. Robinson |
| collection | DOAJ |
| description | Certain algebraic solutions of the Klein-Gordon equation which involve Bessel functions are examined. It is demonstrated that these functions constitute an infinite series, each term of which is the solution of a boundary value problem involving a combination of source functions which comprise delta functions and their derivatives to infinite order. In addition, solutions to the homogeneous equation are constructed which comprise a continuous spectrum over non-integer order. These solutions are discussed in the context of wave propagation in isotropic cold plasma and the atmosphere. |
| first_indexed | 2024-04-13T06:23:10Z |
| format | Article |
| id | doaj.art-e780917f01ab4fd98de58c99a5c86ad7 |
| institution | Directory Open Access Journal |
| issn | 0992-7689 1432-0576 |
| language | English |
| last_indexed | 2024-04-13T06:23:10Z |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Annales Geophysicae |
| spelling | doaj.art-e780917f01ab4fd98de58c99a5c86ad72022-12-22T02:58:34ZengCopernicus PublicationsAnnales Geophysicae0992-76891432-0576122/3220225A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphereT. R. RobinsonCertain algebraic solutions of the Klein-Gordon equation which involve Bessel functions are examined. It is demonstrated that these functions constitute an infinite series, each term of which is the solution of a boundary value problem involving a combination of source functions which comprise delta functions and their derivatives to infinite order. In addition, solutions to the homogeneous equation are constructed which comprise a continuous spectrum over non-integer order. These solutions are discussed in the context of wave propagation in isotropic cold plasma and the atmosphere.http://www.ann-geophys.net/12/220/1994/angeo-12-220-1994.html |
| spellingShingle | T. R. Robinson A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere Annales Geophysicae |
| title | A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere |
| title_full | A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere |
| title_fullStr | A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere |
| title_full_unstemmed | A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere |
| title_short | A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere |
| title_sort | note on the klein gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere |
| url | http://www.ann-geophys.net/12/220/1994/angeo-12-220-1994.html |
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