Interaction of solitons on 2-dimensional branched [pi]-electron surface of graphene ribbons

We have performed quantum-mechanical study of charge distribution on the carbon atoms of two-dimensional conjugated system of the model graphene ribbon. The study shows that charges in the quasi-two dimensional conjugated system of the graphene ribbon are not localized on separate carbon atoms, but form one-dimensional solitonic charge waves along zig-zag sides. There are two solitonic charge waves in the dication or dication due to generation of own soliton by each charge; the first soliton in the acene chain is located on one side while the second one is positioned on the opposite side. The shapes of the solitonic waves in the graphene ribbon are similar to ones in one-dimensional conjugated systems. Similarly, in the ionic two-dimensional collective systems of π-electrons two splitted solitonic levels are generated; lengthening of the chain leads to convergence of the levels. The widening of graphene ribbon (y-expansion of two-dimensional conjugated system is accompanied with recession of both solitons to outer sides, so amplitudes of the solitons on the inner sides regularly decrease under widening of the model graphene ribbon; the charges on the inner carbon atoms converge to zero.