Year: 2010
Type: article
Abstract: The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the Korteweg–de Vries (KdV) hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, we show that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlevé equation.
Source: Nonlinearity
Authors: Emilio Musso, Lorenzo Nicolodi
Institutions: Politecnico di Torino, University of Parma
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2126399288