2020/08/12 by Z. E. Musielak, Musielak, Z. E.
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Nonlinear Waves and Solitons #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.2008.05562
Null Lagrangians and their gauge functions are derived for given standard and non-standard Lagrangians. The obtained standard null Lagrangians generalize those previously found but the non-standard null Lagrangians are new. The gauge functions are used to make the action invariant and introduce the exact null Lagrangians, which form a new family of null Lagrangians. The conditions required for the action to be invariant are derived for all null Lagrangians presented in this paper, thus, making them exact. As a specific application, the exact null Lagrangians are derived for a second-order ordinary differential equation. The application shows that the exact null Lagrangians can be obtained for any ordinary differential equation with known Lagrangian.