Asymptotics of a finite-energy unidirectional solution of the wave equation with non-spherical-wave behavior at infinity
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
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.