  The leading-twist parton distribution functions of the pion and kaon are
calculated for the first time using a rainbow-ladder truncation of QCD's
Dyson-Schwinger equations (DSEs) that self-consistently sums all planar
diagrams. The non-perturbative gluon dressing of the quarks is thereby
correctly accounted for, which in practice means solving the inhomogeneous
Bethe-Salpeter equation (BSE) for the quark operator that defines the
spin-independent quark distribution functions. An immediate consequence of
using this dressed vertex is that gluons carry 35% of the pion's and 30% of the
kaon's light-cone momentum, with the remaining momentum carried by the quarks.
The scale associated with these DSE results is $\mu_0 = 0.78\,$GeV. The gluon
effects generated by the inhomogeneous BSE are inherently non-perturbative and
cannot be mimicked by the perturbative QCD evolution equations. A key
consequence of this gluon dressing is that the valence quarks have reduced
support at low-to-intermediate $x$, where the gluons dominate, and increased
support at large $x$. As a result, our DSE calculation of the pion's valence
quark distribution is in excellent agreement with the Conway et al.
pion-induced Drell-Yan data, but nevertheless exhibits the $q_\pi(x) \simeq
(1-x)^2$ behavior as $x\to 1$ predicted by perturbative QCD.
