Methods of analysis of resonance shock structures in low-dissipative media with dispersion

Investigation of generalized Korteweg–Burhgers equation showed that three types of shock structures are observed for low-dissipative media with dispersion and nonlinearity. Stationary low-dissipative structures may contain internal non-dissipative structures. These structures are transitions between uniform and wave states. Not only one shock structure may be found. This fact leads to hysteresis. Shock structure depends on the way of evolution of the system. Analysis of all types of shock structures for the system under consideration is fulfilled. Correspondence between shock structure types and bifurcations of brunches of stationary solutions is found.