Applications of a nonlinear evolution equation I: The parton distributions in the proton distributions in the proton

The nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations with parton recombination corrections are used to dynamically evaluate the proton's parton distribution functions starting from a low scale μ², where the nucleon consists of valence quarks. We find that the resulting negative nonlinear corrections can improve the perturbative stability of the QCD evolution equation at low Q². Our resulting parton distributions, with four free parameters, are compatible with the existing databases. This approach provides a powerful tool to connect the quark models of the hadron and various nonperturbative effects at the scale μ with the measured structure functions at the high scale Q² 蠑 μ².