Heat bullets

TL;DR

This paper introduces new localized solutions for the 3D heat equation using Airy, Gaussian, and Bessel functions, which propagate while maintaining their shape, akin to heat analogues of optical Airy bullets.

Contribution

It presents novel analytical solutions for the 3D heat equation that combine Airy, Gaussian, and Bessel functions, enhancing understanding of localized heat propagation.

Findings

Solutions propagate with acceleration along their direction

They retain their Gaussian or Bessel structure orthogonal to propagation

These solutions serve as heat analogues of Airy light bullets

Abstract

New localized structured solutions for the three-dimensional linear diffusion (heat) equation are presented. These new solutions are written in terms of Airy functions and either Gaussian or Bessel functions. They accelerate along their propagation direction, while in the plane orthogonal to it, they retain their either Gaussian or Bessel structure. These diffusion (heat) densities retain a localized structure in space as they propagate, and may be considered the heat analogue of Airy light bullets.