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We find exact solutions of the string equations of motion and constraintsdescribing the {\em classical}\ splitting of a string into two. We show thatfor the same Cauchy data, the strings that split have {\bf smaller} action thanthe string without splitting. This phenomenon is already present in flatspace-time. The mass, energy and momentum carried out by the strings arecomputed. We show that the splitting solution describes a natural decay processof one string of mass $M$ into two strings with a smaller total mass and somekinetic energy. The standard non-splitting solution is contained as aparticular case. We also describe the splitting of a closed string in thebackground of a singular gravitational plane wave, and show how the presence ofthe strong gravitational field increases (and amplifies by an overall factor)the negative difference between the action of the splitting and non-splittingsolutions.Comment: 27 pages, revtex

Classical splitting of fundamental strings