# Generation of shock waves from localized sources: The case of the Burgers equation

## TL;DR

This paper demonstrates that shock waves in the Burgers equation can originate from localized sources, which follow a unique evolution equation featuring both single-soliton and localized-hump solutions.

## Contribution

It introduces a novel source evolution equation for the Burgers equation that admits both soliton and hump solutions, explaining shock wave generation from localized sources.

## Key findings

- Shock waves can be generated from localized sources in the Burgers equation.
- The source evolution equation has a single-soliton solution.
- The source evolution equation admits an infinite family of localized-hump solutions.

## Abstract

It is shown that the shock wave solutions of the Burgers equation can be generated from localized sources. The evolution equation obeyed by the sources has a novel characteristic: It has a single-soliton solution as well as an infinite family of localized-hump solutions.

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Source: https://tomesphere.com/paper/1908.01315