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On a p-adic wave equation

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Abstract

It is shown that a “p-adic plane wave” f(t + ω 1 x 1 + ... + ω n x n ), (t, x 1, ..., x n ) ∈ ℚ n + 1 p , where f is a Bruhat-Schwartz complex-valued test function and max1≤j≤n |ω 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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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, Kiev, 01601, Ukraine

    Anatoly N. Kochubei

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  1. Anatoly N. Kochubei
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Correspondence to Anatoly N. Kochubei.

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Kochubei, A.N. On a p-adic wave equation. Proc. Steklov Inst. Math. 265, 143–147 (2009). https://doi.org/10.1134/S0081543809020138

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  • DOI: https://doi.org/10.1134/S0081543809020138

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