# Rogue Heat and Diffusion Waves

## TL;DR

This paper demonstrates through numerical simulations that nonlinear heat and diffusion models can produce rogue waves characterized by large fluctuations due to modulation instability, with implications across various scientific fields.

## Contribution

It introduces the concept of rogue heat and diffusion waves generated by modulation instability in nonlinear models, expanding understanding of fluctuation phenomena in these systems.

## Key findings

- Rogue heat and diffusion waves can form in nonlinear models.
- Modulation instability causes large fluctuations in these systems.
- Potential applications span multiple scientific disciplines.

## Abstract

In this paper, we numerically show and discuss the existence and characteristics of rogue heat and diffusion waves. More specifically, we use two different nonlinear heat (diffusion) models and show that modulation instability leads to the generation of unexpected and large fluctuations in the frame of these models. These fluctuations can be named as rogue heat (diffusion) waves. We discuss the properties and statistics of such rogue waves. Our results can find many important applications in many branches such as the nonlinear heat transfer, turbulence, financial mathematics, chemical or biological diffusion, nuclear reactions, subsurface water infiltration, and pore water pressure diffusion modeled in the frame of nonlinear Terzaghi consolidation models, just to name a few.