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arXiv · 2509.00773

Asymptotics of a finite-energy unidirectional solution of the wave equation with non-spherical-wave behavior at infinity

Alexandr B. Plachenov·Aleksei P. Kiselev
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Abstract

A detailed investigation is presented of a simple unidirectional finite-energy solution of the 3D wave equation. Its asymptotics as a spatial point runs to infinity with the wave propagations speed is a standard spherical wave as z < 0, where z is a Cartesian coordinate, and has an additional factor logarithmic with respect to the distance as z > 0. Asymptotics for a point running to infinity with an arbitrary constant speed is discussed

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Alexandr B. Plachenov, Aleksei P. Kiselev. 2025-08-31. Asymptotics of a finite-energy unidirectional solution of the wave equation with non-spherical-wave behavior at infinity. https://arxiv.org/abs/2509.00773

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