Methods of analysis of multi-wave shock structures in low-dissipative models with dispersion

Previously developed methods of analysis of non-dissipative and low-dissipative shocks are applied for shocks with resonance states. It is found for the model described by generalized Korteweg–Burgers equation that three types of shock structures are observed: stationary, time-periodic and stochastic. Stationary low-dissipative structures contain internal non-dissipative shock structures. These structures are transitions between one-wave and resonance multi-wave states. Several wave zones of different type are observed for one side of the shock. These zones are described by averaged equations and divided by weak bifurcation type shocks. Shock structure may be not unique. The type of the shock depends on character of evolution of system. General analysis of all shocks for the model under consideration is fulfilled.