In order to provide effective managements of urban bus transport network and serve better for citizen travels, we modelled and simulated the Tai'an city bus lines by space P way, space L way and bus line way with complex network and graph theory. By computing adjacency matrix and complex network topology characters in bus line model, we concluded that the Tai'an city network had small-world character with short average path length and high clustering coefficient. The same results were achieved by complex network characters statistics in space P way and space L way after getting rid of noise. Theoretical analysis and experimental simulation imply that it is feasible and effective for bus line management and citizen travel by modelling and optimisation on bus transport network with complex network characters statistics and analysis.

By considering a discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations are derived. The relation to the Toda type lattice is achieved by variable transformation. With the help of Tu scheme, the Hamiltonian structure of the resulting lattice hierarchy is constructed. The Liouville integrability is then demonstrated. Semi-direct sum of Lie algebras is proposed to construct discrete integrable couplings. As applications, two kinds of discrete integrable couplings of the resulting system are worked out.