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

2025/08/31 by A. B. Plachenov, Plachenov, Alexandr B., A. P. Kiselev +1
Computer Science · Mathematics · #78A40 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Physical sciences #Optics (physics.optics)

paper · pdf · doi:10.48550/arxiv.2509.00773

openalex publication_date 2025/08/31 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

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

Citations

• Wave pulses with unusual asymptotical behavior at infinity
• Unidirectional pulses: relatively undistorted quasi-spherical waves, Fourier-Bessel integrals, and plane-waves decompositions
• Asymptotic properties of solutions to a certain ultrahyperbolic equation

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