Methods of Investigation of the Non-Dissipative Shock with Emission

Methods of investigation of non-dissipative shocks are developed in this paper. These methods are based on numerical analysis of dynamical systems and applied to shocks with emission of generalized Korteweg-de Vries and cold plasma equations. Boundary conditions for the shocks are found without shock structure analysis. Averaged equations for wave zones are derived. The solution for centered simple envelope wave is obtained. Methods of shock structure investigation are developed also. One of these methods implies that the closest to some point trajectory is found. This point is found previously as a point on the cycle, which corresponds to the shock emission. The other method is based on treatment of shock structure with emission as the limiting solution of the sequence of solitary waves with many humps. This method shows that there is enumerable number of shock structures.