Nonspreading solutions of the inhomogeneous scalar wave equation

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Abstract
A simple condition that is necessary and sufficient for the solution of the inhomogeneous wave equation to be a nonspreading wave is derived for a class of driving terms that arise in certain physical problems. The condition is applied to the analysis of the self−scattering of gravitational multipole radiation at second perturbative order. It is proved that there is no scattering at the multipole component of highest order in the second−order gravitational field. It is conjectured that there is no scattering for every component of the second−order field. A mathematical expression of this conjecture, derived from the condition for nonspreading, is given and it implies conjectured identities on Clebsch−Gordan coefficients.

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