  The nonperturbative quantization technique \`{a} la Heisenberg is applied for
non-Abelian gauge theories. The operator Yang-Mills equation is written, which
on the corresponding averaging gives an infinite set of equations for all Green
functions. We split all degrees of freedom into two groups: in the former, we
have $A^a_\mu \in \mathcal G \subset SU(N)$, and in the second group we have
coset degrees of freedom $SU(N) / \mathcal G$. Using such splitting and some
assumptions about 2- and 4-point Green functions, we truncate the infinite set
of equations to two equations. The first equation is for the gauge fields from
the subgroup $\mathcal G$, and the second equation is for a gluon condensate
which is the dispersion of quantum fluctuations of the coset fields. Two
examples are considered: The first one is a flux tube solution describing
longitudinal color electric fields stretched between quark and antiquark
located at the $\pm$ infinities. The second one is a flux tube stretched
between two quarks (antiquarks) located at $\pm \infty$. A special case is
considered when the longitudinal electric field produced by a quark located at
$+ \infty$ is equal and oppositely directed to the field generated by a quark
located at $- \infty$ that leads to zero total electric field. Both solutions
represents the dual Meissner effect: the electric field is pushed out from the
gluon condensate.
