  An array of one-dimensional conductors coupled by transverse hopping and
interaction is studied with the help of a variational wave function. This wave
function is devised as to account for one-dimensional correlation effects. We
show that under broad conditions our system possesses the superconducting
ground state even if no attraction is present. The superconducting mechanism is
of many-body nature and deviates substantially from BCS. The phase diagram of
the model is mapped. It consists of two ordered phases competing against each
other: density wave, spin or charge, and unconventional superconductivity.
These phases are separated by the first order transition. The symmetry of the
superconducting order parameter is a non-universal property. It depends on
particulars of the Hamiltonian. Within the framework of our model possible
choices are the triplet $f$-wave and the singlet $d_{xy}$-wave. Organic
quasi-one-dimensional superconductors have similar phase diagram.
