A Non-Archimedean Wave Equation

2007/07/18 by Anatoly N. Kochubei, Kochubei, Anatoly N. · 1 citation
Mathematics · Physics and Astronomy · Medicine · #advanced mathematical theories #Quantum Mechanics and Applications #Biofield Effects and Biophysics

paper · pdf · doi:10.48550/arxiv.0707.2653

Abstract

Let K be a non-Archimedean local field with the normalized absolute value |⋅ |. It is shown that a ``plane wave'' f(t+ω₁ x₁+... +ω_nx_n), where f is a Bruhat-Schwartz complex-valued test function on K, (t,x₁,..., x_n)∈ Kⁿ⁺¹, max_{1≤ j≤ n}|ω_j|=1, satisfies, for any f, a certain homogeneous pseudo-differential equation, an analog of the classical wave equation. A theory of the Cauchy problem for this equation is developed.

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