Conservation laws of the one-dimensional relativistic magnetogasdynamics equations

Abstract The present paper offers a comprehensive analysis of the one-dimensional relativistic magnetogasdynamics equations in Lagrangian coordinates. These equations, describing the behavior of a relativistic magnetized gas, are reformulated in variational form to facilitate further analysis. A complete group analysis of the resulting Euler–Lagrange equation is performed, allowing us to systematically identify the symmetries inherent in the system. Using Noether’s theorem, we derive conservation laws in Lagrangian coordinates, offering critical insights into the invariants and conserved quantities of the system. This work expands the theoretical understanding of relativistic magnetogasdynamics.