A NOTE ON THE KLEIN-GORDON EQUATION AND ITS SOLUTIONS WITH APPLICATIONS TO CERTAIN BOUNDARY-VALUE-PROBLEMS INVOLVING WAVES IN PLASMA AND INTHE ATMOSPHERE
Tr. Robinson, A NOTE ON THE KLEIN-GORDON EQUATION AND ITS SOLUTIONS WITH APPLICATIONS TO CERTAIN BOUNDARY-VALUE-PROBLEMS INVOLVING WAVES IN PLASMA AND INTHE ATMOSPHERE, Annales geophysicae, 12(2-3), 1994, pp. 220-225
Certain algebraic solutions of the Klein-Gordon equation which involve
Bessel functions are examined. It is demonstrated that these function
s 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 w
hich comprise a continuous spectrum over non-integer order. These solu
tions are discussed in the context of wave propagation in isotropic co
ld plasma and the atmosphere.