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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Volume 12, issue 2/3
Ann. Geophys., 12, 220–225, 1994
https://doi.org/10.1007/s00585-994-0220-3
© European Geosciences Union 1994
Ann. Geophys., 12, 220–225, 1994
https://doi.org/10.1007/s00585-994-0220-3
© European Geosciences Union 1994

  31 Jan 1994

31 Jan 1994

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

T. R. Robinson T. R. Robinson

Abstract. 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.

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