Interactions of Elementary Waves for the Asymmetric Keyfitz-Kranzer System

The interactions of elementary waves for the asymmetrical Keyfitz-Kranzer system under the conditions of
generalized Chaplygin gas and modified Chaplygin gas were studied respectively. For the former case, its Riemann solution is made up of three different structures R+ J, S+J or delta waves. For the modified Chaplygin gas, its solution is made up of R+J and S+J. Since the initial condition is the three normal states, depending on the different value ranges and by use of the
characteristic analysis and phase plane analysis, the interactions of the elementary waves are examined under different situations, and structurally, the global solutions are acquired. By ordering the parameter approximates to zero, it can be found that the Riemann solutions are stable for such perturbations under the initial conditions.