Meromorphic solutions of nonlinear ordinary differential equations

TL;DR

This paper examines the use of Laurent series to analyze exact solutions of nonlinear ordinary differential equations, revealing that many solution methods are fundamentally similar and yield the same solutions.

Contribution

It demonstrates that various existing methods for solving nonlinear ODEs are essentially equivalent when viewed through Laurent series analysis.

Findings

Most solution methods are conceptually identical.

Different methods produce the same solutions.

Laurent series provide insight into solution structures.

Abstract

Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of many methods for finding exact solutions. We show that most of these methods are conceptually identical to one another and they allow us to have only the same solutions of nonlinear ordinary differential equations.