The solution of two dimensional nonlinear wave equation in a class of discontinuous functions

In this thesis, a new method is developed to obtain the exact solution of the Cauchy problem for the two dimensional quasilinear partial differential equation.In the second part, the exact solution of the initial value problem for the equation with constant coefficient is found and its some properties are investigated. To do so, two auxiliary problems which have some advantages on the main problem are introduced, and by using these advantages the exact solution of the main problem is obtained.In the third part of the thesis, the obtained results are extended to the two dimensional quasi linear Hopf equation.Finally, the Cauchy problem for the first order nonlinear partial differential equation having non-convex state function is presented and its exact solution is derived.