Parametric solution of certain nonlinear differential equations in cosmology

TL;DR

This paper derives explicit parametric solutions for specific nonlinear differential equations relevant to cosmology and Bose-Einstein condensates using elliptic functions, providing a mathematical framework for these models.

Contribution

It introduces a novel explicit parametrized solution for certain nonlinear differential equations in cosmology using elliptic functions.

Findings

Explicit solutions expressed via Weierstrass elliptic functions.

Applicable to both homogeneous and inhomogeneous cosmological models.

Connects cosmological equations with Bose-Einstein condensate dynamics.

Abstract

We obtain in terms of the Weierstrass elliptic $\wp-$function, sigma function, and zeta function an explicit parametrized solution of a particular nonlinear, ordinary differential equation. This equation includes, in special cases, equations that occur in the study of both homogeneous and inhomogeneous cosmological models, and also in the dynamic Bose-Einstein condensates - cosmology correspondence, for example.