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.

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.