We elucidate the self-evolution of two Bose gases from a strongly non - equilibrium initial state. Large scale numerical simulations of the coupled nonlinear Schrödinger (NLS) equations are used to follow the evolution of the system from weak turbulence to strong turbulence to superfluid turbulence in the long-wavelength region of energy space with a formation of a tangle of topological defects. The addition of the second gas increases the number of condensed particles in the first gas. It is shown that the large wavelength part of the fields evolves into coherent structures identified as solitary wave complexes of the coupled nonlinear Schrödinger equations. The families of the solitary waves moving on uniform background or along the topological defects are obtained as solutions of the coupled Gross-Pitaevskii equations. It is shown that there exist three continuous families of such solutions with or without the cusp in energy-momentum space.