Integrable system of null curve and Betchov-Da Rios equation

Abstract

This study focuses on the time evolution of a null curve using a new frame and a new transformation in Minkowski 3-space. Accordingly, Landau-Lifshitz and coupled Boussinesq-like equations for the null curve are provided in terms of the new transformation. Additionally, a null Betchov-Da Rios equation along the null curve is considered to study new soliton solutions to the null Betchov-Da Rios equation. Finally, the corresponding evolution surfaces of the Hasimoto surface are investigated along the null curve in Minkowski 3-space.