arXiv subjects

Alexandr B. Plachenov

Publications and source records attributed to Alexandr B. Plachenov.

2 recordsLinked to original sources

arXiv2025

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

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

physics.optics↗

arXiv2024

Unidirectional pulses: relatively undistorted quasi-spherical waves, Fourier-Bessel integrals, and plane-waves decompositions

A theoretical description of a class of unidirectional axisymmetric localized pulses, is given. The equivalence of their representations in the form of relatively undistorted quasi-spherical waves, in the form of Fourier-Bessel integrals and in the form of a superposition of plane waves with wave vectors having positive projections on a given direction is established.

math.GM↗