The weak solution of 1. order nonlinear system of differantial equations and riemann ınvariants

In this thesis the system of quasi - linear differential equations is investigated. It is known that method of characteristics is the key to the solution of the Cauchy problem for 1.order partial differential equations. But, it is impossible to apply the method of characteristic to the solution of system of differential equations. For this aim the concept of Riemann invariants are introduced. Using the Riemann?s invariants, each equation of the system could be reduced to an ordinary differential equation.In the second part of this thesis the condition for obtaining the characteristics is suggested then using this conditions, the Riemann invariants for some System of differential equations are found