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Based on the field theory of density fluctuation under Newtonian gravity, weobtain analytically the nonlinear equation of 3-pt correlation function $\zeta$of galaxies in a homogeneous, isotropic, static universe. The densityfluctuations have been kept up to second order. By the Fry-Peebles ansatz andthe Groth-Peebles ansatz, the equation of $\zeta$ becomes closed and differsfrom the Gaussian approximate equation. Using the boundary condition inferredfrom the data of SDSS, we obtain the solution $\zeta(r, u, \theta)$ at fixed$u=2$, which exhibits a shallow $U$-shape along the angle $\theta$ and,nevertheless, decreases monotonously along the radial $r$. We show itsdifference with the Gaussian solution. As a direct criterion ofnon-Gaussianity, the reduced $Q(r, u, \theta)$ deviates from the Gaussianityplane $Q=1$, exhibits a deeper $U$-shape along $\theta$ and varies weakly along$r$, agreeing with the observed data.

The nonlinear field equation of the three-point correlation function of galaxies