Geodesic
On a~$p$-adic Wave Equation
Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 154-158.

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It is shown that a "$p$-adic plane wave" $f(t+\omega_1x_1+\dots+\omega_nx_n)$, $(t,x_1,\dots,x_n)\in\mathbb Q_p^{n+1}$, where $f$ is a Bruhat–Schwartz complex-valued test function and $\max_{1\le j\le n}|\omega_j|_p=1$, satisfies, for any $f$, a certain homogeneous pseudodifferential equation, an analog of the classical wave equation. A theory of the Cauchy problem for this equation is developed. 
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A. N. Kochubei. On a~$p$-adic Wave Equation. Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 154-158. http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a12/

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