Special Ulrich bundles on regular Weierstrass fibrations

The main goal of this short paper is to prove the existence of rank 2 simple and special Ulrich bundles on a wide class of elliptic surfaces: namely, on regular Weierstrass fibrations π: S→ P1. Alongside we also show the existence of rank 2 weakly Ulrich sheaves on arbitrary Weierstrass fibrations S→ C and we deal with the (non-)existence of rank one Ulrich bundles on them