Open AccessA note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere
Author(s) -
T. R. Robinson
Publication year - 1994
Publication title -
annales geophysicae
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.522
H-Index - 93
eISSN - 1432-0576
pISSN - 0992-7689
DOI - 10.1007/s00585-994-0220-3
Subject(s) - bessel function , boundary value problem , mathematical analysis , context (archaeology) , wave equation , physics , mathematics , isotropy , quantum mechanics , paleontology , biology
Certain algebraic solutions of theKlein-Gordon equation which involve Bessel functions are examined. It isdemonstrated that these functions constitute an infinite series, each term ofwhich is the solution of a boundary value problem involving a combination ofsource functions which comprise delta functions and their derivatives toinfinite order. In addition, solutions to the homogeneous equation areconstructed which comprise a continuous spectrum over non-integer order. Thesesolutions are discussed in the context of wave propagation in isotropic coldplasma and the atmosphere