Integrability aspects of the vortex filament equation for pseudo-null curves

TL;DR

This paper explores the integrability of pseudo-null curve motions in Lorentzian space, linking them to Burgers' equation and providing a recursion operator to analyze their properties.

Contribution

It develops an algebraic framework for pseudo-null curves, connects their motion to Burgers' equation, and introduces a recursion operator for the pseudo-null vortex filament equation.

Findings

Established a connection between pseudo-null vortex filament equation and Burgers' equation.

Developed an algebraic approach for studying pseudo-null curve motions.

Provided a recursion operator to analyze integrability properties.

Abstract

An algebraic background in order to study the integrability properties of pseudo-null curve motions in a $3$-dimensional Lorentzian space form is developed. As an application we delve into the relationship between the Burgers' equation and the pseudo-null vortex filament equation. A recursion operator for the pseudo-null vortex filament equation is also provided.