  The interaction of laser radiation with single J aggregates of cyanine dyes
is theoretically analyzed and numerically simulated. The quantum mechanical
calculations of the equilibrium geometry and the energies and intensities of
the lowest singlet electronic transitions in pseudoisocyanine chloride and its
linear (chain) oligomers are fulfilled. The data of these calculations can
serve as parameters of the analyzed model of interaction of J aggregates with
radiation in the oneparticle density matrix approximation. This model takes
into account relaxation processes, the annihilation of excitations at
neighboring molecules, and inho mogeneous broadening. Assuming that the
inhomogeneous broadening is absent, calculations demonstrate the existence of
spatial bistability, molecular switching waves, and dissipative solitons. The
effect of the inhomogeneous broadening and the radiation intensity on the
effective coherence length in linear (chain) J aggregates is analyzed
