Analytical solutions of the time evolution equation for inelastic null curves

This study investigates the inextensible flows of null Cartan curves in R21 Minkowski space. The tangent, normal, and binormal velocity components of null Cartan curves are analyzed in detail, and their interrelationships are revealed. The main aim of the study is to construct a family of inextensible null Cartan curves from the initial null Cartan curve. In this process, the torsion and time evolution equations of the curves are solved using the Korteweg-de Vries (KdV) equation. The obtained solutions are numerically visualized and interpreted. Additionally, an application is presented for the inextensible flows of the null Cartan curve moving with constant normal acceleration.