  During the eighties several physical models using p-adic numbers were
proposed. Particularly various models of p-adic quantum mechanics. As a
consequence of this fact several new mathematical problems emerged, among them,
the study of p-adic pseudo-differential equations. In this paper we initiate
the study of the decay of the solutions of wave-type pseudo-differential
equations over p-adic fields; these equations were introduced by Kochubei in
connection with the problem of characterizing the p-adic wave functions using
pseudo-differential operators. We show that the solutions of p-adic wave-type
equations have a decay similar to the solutions of classical generalized wave
equations.
