Classes of second order nonlinear partial differential equations reducible to first order

Abstract

In this paper, we present new techniques for solving a large variety of partial differential equations. The proposed method reduces the PDEs to first order differential equations known as classical equations such as Bernoulli, Ricatti and Abel equations. The main idea is based on implementing new techniques by combining variations of parameters with characteristic methods to obtain many new and general exact solutions. In each class of PDE's, we give illustrated examples. Moreover, the method presented in this paper can be easily extended to classes of second order nonlinear PDEs.