arXiv subjects

Noureddine Mhadhbi

Publications and source records attributed to Noureddine Mhadhbi.

2 recordsLinked to original sources

arXiv2023

Exact Solutions for Nonlinear Partial Differential Equations: A Fusion of Classical Methods and Innovative Approaches

This article demonstrates how variation of parameters can be successfully implemented in combination with other classical techniques, such as the method of characteristics, to derive novel classes of solutions to nonlinear partial differential equations (NLPDES) by considering specific initial conditions. This innovative approach offers the advantage of generating exact solutions. The results underscore this method's potential to address additional NLPDE classes.

math.AP↗

arXiv2023

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

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.

math.AP↗