Exact solutions of classes of second order nonlinear partial differential equations reducible to first order

Abstract

This paper illustrates the successful implementation of the method of variation of parameters in combination with the method of characteristics and other techniques to obtain exact solutions for a wide range of partial differential equations. The proposed approach reduces partial differential equations (PDEs) to first-order differential equations, referred to as classical equations, including Bernoulli, Ricatti, and Abel equations. In addition, the techniques proposed have the ability to produce precise solutions for nonlinear second order PDEs. For each PDE class, the method's effectiveness is demonstrated through illustrative examples.