The effect of finite duration sources on modes and generalization of the d'Alembert solution
Analysis of PDEs
2025-05-22 v2 Mathematical Physics
math.MP
Atmospheric and Oceanic Physics
Applied Physics
Classical Physics
Optics
Abstract
We investigate the evolution of dispersive waves governed by linear wave equations, where a finite duration source is applied. The resulting wave may be viewed as the superposition of modes before the source is turned on and after it is turned off. We consider the problem of relating the modes after the source term is turned off to the modes before the source term was turned on. We obtain explicit formulas in both the wavenumber and position representations. A number of special cases are considered. Using the methods presented, we obtain a generalization of the d'Alembert solution which applies to linear wave equations with constant coefficients.
Keywords
Cite
@article{arxiv.2504.20302,
title = {The effect of finite duration sources on modes and generalization of the d'Alembert solution},
author = {J. S. Ben-Benjamin and L. Cohen},
journal= {arXiv preprint arXiv:2504.20302},
year = {2025}
}