  The temperature dependence of the two superconducting gaps in pressurised
H_3S at 155 GPa with a critical temperature of 203 K has been determined by
data analysis of the experimental curve of the upper critical magnetic field as
a function of temperature in the framework of the two bands s-wave Eliashberg
theory, with two different phonon mediated intra-band Cooper pairing channels
in a regime of moderate strong couplings with the key role of the pair exchange
interaction between the two gaps giving the two non-diagonal terms of the
coupling tensor which are missing in the single band s wave Eliashberg theory.
The results provide the prediction of the different temperature dependence of
the small and large gaps as a function of temperature which provide evidence of
multi-gap superconductivity in H_3S.
