Meromorphic solutions of a third order nonlinear differential equation

TL;DR

This paper classifies all meromorphic solutions of a specific third-order nonlinear differential equation, proving they are elliptic or degenerate elliptic, and explicitly constructing these solutions.

Contribution

It provides a complete classification and explicit construction of meromorphic solutions for a particular third-order nonlinear differential equation.

Findings

All solutions are elliptic or degenerate elliptic.

Explicit forms of solutions are constructed.

The classification advances understanding of nonlinear differential equations.

Abstract

We prove that all the meromorphic solutions of the nonlinear differential equation c0 u"' + 6 u^4 + c1 u" + c2 u u' + c3 u^3 + c4 u'+ c5 u^2 + c6 u +c7=0 are elliptic or degenerate elliptic, and we build them explicitly.