We present a statistical equilibrium model of self-organization in a
class of focusing, nonintegrable nonlinear Schr\"{o}dinger (NLS)
equations. The theory predicts that the asymptotic--time behavior of
the NLS system is characterized by the formation and persistence of a
large--scale coherent solitary wave, which minimizes the Hamiltonian
given the conserved particle number ($L^2$-norm squared), coupled with
small--scale random fluctuations, or radiation. The fluctuations
account for the difference between the conserved value of the
Hamiltonian and the Hamiltonian of the coherent state. The
predictions of the statistical theory are tested against the results
of direct numerical simulations of NLS, and excellent qualitative and
quantitative agreement is demonstrated.
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