Charged rotating black string in gravitating nonlinear electromagnetic fields

We obtain a new solution of rotating black string coupled to a nonlinear electromagnetic field in the background of anti-de Sitter spaces. We consider two types of nonlinear electromagnetic Lagrangians, namely, logarithmic and exponential forms. We investigate the geometric effects of nonlinearity parameter and find that for large r, these solutions recover the rotating black string solutions of Einstein-Maxwell theory. We calculate the conserved and thermodynamic quantities of the rotating black string. We also analyze thermodynamics of the spacetime and verify the validity of the first law of thermodynamics for the obtained solutions.