  Considering both the Gauss-Bonnet and the Born-Infeld terms, which are on
similar footing with regard to string corrections on the gravity side and
electrodynamic side, we present a new class of rotating solutions in
Gauss-Bonnet gravity with $k$ rotation parameters in the presence of a
nonlinear electromagnetic field. These solutions, which are asymptotically
anti-de Sitter in the presence of cosmological constant, may be interpreted as
black brane solutions with inner and outer event horizons, an extreme black
brane or naked singularity provided the metric parameters are chosen suitably.
We calculate the finite action and conserved quantities of the solutions by
using the counterterm method, and find that these quantities do not depend on
the Gauss-Bonnet parameter. We also compute the temperature, the angular
velocities, the electric charge and the electric potential. Then, we calculate
the entropy of the black brane through the use of Gibbs-Duhem relation and show
that it obeys the area law of entropy. We obtain a Smarr-type formula for the
mass as a function of the entropy, the angular momenta and the charge, and show
that the conserved and thermodynamic quantities satisfy the first law of
thermodynamics. Finally, we perform a stability analysis in both the canonical
and grand-canonical ensemble and show that the presence of a nonlinear
electromagnetic field has no effect on the stability of the black branes, and
they are stable in the whole phase space.
