An exact solution for a non-autonomous delay differential equation
arXiv:2411.11402 · doi:10.1137/25M1738164
Abstract
We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit solution for non-autonomous DDEs and is a rare example even among general DDEs. The constructed solution offers key physical insights and facilitates the analysis of system properties, such as the envelope profile of the dynamics.
16 pages, 8 figures, shorter version submitted for publication; ver.2. Fixed some technical errors; ver.3. Fixed some technical errors; ver.4 Fixed some technical erros, adding more references