  We investigated the nonlinear Meissner effect (NLME) in Nb$_3$Sn thin film
coplanar resonators by measuring the resonance frequency as a function of a
parallel magnetic field at different temperatures. We used low rf power probing
in films thinner than the London penetration depth $\lambda(B)$ to
significantly increase the field onset of vortex penetration and measure the
NLME under equilibrium conditions. Contrary to the conventional quadratic
increase of $\lambda(B)$ with $B$ expected in s-wave superconductors, we
observed a nearly linear increase of the penetration depth with $B$. We
concluded that this behavior of $\lambda(B)$ is due to weak linked grain
boundaries in our polycrystalline Nb$_3$Sn films, which can mimic the NLME
expected in a clean d-wave superconductor.
