Articles | Volume 12, issue 2/3
https://doi.org/10.1007/s00585-994-0220-3
https://doi.org/10.1007/s00585-994-0220-3
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

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.