Explicit expressions for meromorphic solution of autonomous nonlinear ordinary differential equations

TL;DR

This paper develops an algorithm to explicitly construct meromorphic solutions, including rational, periodic, and elliptic types, for a broad class of autonomous nonlinear ordinary differential equations.

Contribution

It provides general explicit expressions for meromorphic solutions of autonomous nonlinear ODEs, expanding the toolkit for solving such equations.

Findings

Derived explicit formulas for meromorphic solutions

Included rational, periodic, and elliptic solutions

Applicable to a wide class of autonomous nonlinear ODEs

Abstract

Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational, periodic, elliptic) are found for a wide class of autonomous nonlinear ordinary differential equations.