On one of methods for finding exact solutions of nonlinear differential equations

TL;DR

This paper reviews an old method for solving nonlinear differential equations, discusses its modifications, and demonstrates its effectiveness through applications to the Fisher equation and a seventh-order nonlinear ODE.

Contribution

It provides a detailed analysis of a classical method, including modifications and practical applications, highlighting its effectiveness and discussing its advantages and disadvantages.

Findings

Effective for solving nonlinear differential equations

Successfully applied to Fisher equation and seventh-order ODE

Discusses merits and demerits of the method

Abstract

One of old methods for finding exact solutions of nonlinear differential equations is considered. Modifications of the method are discussed. Application of the method is illustrated for finding exact solutions of the Fisher equation and nonlinear ordinary differential equation of the seven order. It is shown that the method is one of the most effective approaches for finding exact solutions of nonlinear differential equations. Merits and demerits of the method are discussed.