Covariant hodograph transformations between nonlocal short pulse models and the AKNS(−1) system

The paper presents hodograph transformations between nonlocal short pulse models and the first member in the Ablowitz-Kaup-Newell-Segur negative hierarchy (AKNS(−1)). Multi-component cases are also considered. It is shown that the independent variables of the short pulse models and AKNS(−1) that are connected via hodograph transformations are covariant in nonlocal reductions.