Abstract
The popular Belousov–Zhabotinskii (BZ) system of equations for description of a two component reaction is considered. The Painlevé test is applied to determine integrability of this system. It is shown that the system of equations is nonintegrable in general case. The parameter values of the mathematical model are found for the case when the system of equations passes the Painlevé test. Simplest solutions of the system of equations are presented. Additional conditions are specified when the general solutions of the system can be found. These general solutions are found using the new generalized method for finding exact solutions and the first integrals. Two first integrals of the Belousov–Zhabotinskii reaction system are given at additional conditions on parameter values for the mathematical model.
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