  Originally proposed by Read [1] and Jain [2], the so-called
"composite-fermion" is a phenomenological attachment of two infinitely thin
local flux quanta seen as nonlocal vortices to two-dimensional (2D) electrons
embedded in a strong orthogonal magnetic field. In this letter, it is described
as a highly-nonlinear and coherent mean-field quantum process of the soliton
type by use of a 2D stationary Schroedinger-Poisson differential model with
only two Coulomb-interacting electrons. At filling factor $\nu={1}{3}$ of the
lowest Landau level, it agrees with both the exact two-electron antisymmetric
Schroedinger wave function and Laughlin's Jastrow-type guess for the fractional
quantum Hall effect, hence providing this later with a tentative physical
justification based on first principles.
