Analytical Methods for Solving First-order Nonlinear Partial Differential Equations

Abstract

This research aims to study analytical methods to find the complete solution to nonlinear partial differential equations, the first rank is: (Cauchy’s Method of characteristics), (Charpers” Method) and (Jacobi's Method) in terms of deducting the method and applying it on some examples found that Cauchy’s method is considered the basis for other methods, and this method requites an initial curve given, but in the absence of this curve, the Charpy method is used, and in particular I studied the Jacobi Method because it is easy to generalize to the equation (2n) if variables in the following formula:  and the attached equations are  provide some notes in addition to the necessary definitions and concepts.