Riemann invariants and the solutions of the hyperbolic equations and systems of equations

In this thesis, the solutions of the first order hyperbolic systems of equation using characteristics method are examined. To this end, in the first part of the thesis, the conditions which can be set for the hyperbolic equations and systems equations are examined.In the second part of the thesis, the characteristics method are applied in order to solve the systems of partial differential equations with constant coefficients, the exact solutions are obtained for some class of systems of equation which are of practical importance.In the final part of the thesis, a method is developed to solve the exact solution of the systems of nonlinear equation which model the isentropic and constant entropic flow of ideal gases.