Covariant hodograph transformations between nonlocal short pulse models and AKNS$(-1)$ system

Abstract: The paper presents hodograph transformation between nonlocal short pulse models and the first member in the AKNS negative hierarchy (AKNS($-1$)). We consider real and complex multi-component cases. It is shown that the independent variables of the short pulse models and AKNS($-1$) that are connected via hodograph transformation are covariant in nonlocal reductions.