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arXiv · 2411.11402

An exact solution for a non-autonomous delay differential equation

Kenta Ohira
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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.

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Kenta Ohira. 2024-11-18. An exact solution for a non-autonomous delay differential equation. https://doi.org/10.1137/25m1738164

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