Integrability of a nonlinear evolution equation derived from isoperimetric plane curve motion

TL;DR

This paper explores the geometric interpretation and integrability properties of a third-order nonlinear evolution equation related to isoperimetric plane curve motion, including its bi-Hamiltonian structure and connections to integrable systems.

Contribution

It offers a geometric perspective on transformations linking the equation to the mKdV and analyzes its bi-Hamiltonian integrability and related integrable equations.

Findings

Provides a geometric interpretation of transformation series

Establishes bi-Hamiltonian integrability of the equation

Identifies related integrable equations

Abstract

We provide a geometrical interpretation for the series of transformations used by Sakovich to map the third-order nonlinear evolution equation obtained by Chou and Qu to the mKdV equation. We also discuss its bi-Hamiltonian integrability as well as integrable equations associated with this system.