  The nonlinear electrodynamics proposed by Bandos, Lechner, Sorokin and
Townsend is a remarkable theory that unifies Maxwell, Bialynicki-Birula and
ModMax theories, which are known theories invariant under conformal
transformations and electromagnetic duality transformations. In the
Bandos-Lechner-Sorokin-Townsend nonlinear electrodynamics, we calculate the
energy flux density, dispersion relations, refractive indices, phase and group
velocities of plane waves as well as the changes of the photon wavelength in
the Compton scattering process in the presence of a constant uniform
electromagnetic background. Our results are useful for testing and constraining
this new theory of nonlinear electrodynamics.
