Korteweg-de Vries adiabatic index solitons in barotropic open FRW cosmologies

TL;DR

This paper explores the mathematical connection between the Riccati equation for the Hubble parameter and the Korteweg-de Vries equation for solitons in barotropic open FRW cosmologies, revealing new integrability properties.

Contribution

It demonstrates how the Riccati equation relates to Korteweg-de Vries solitons and shows embedding of discrete adiabatic indices in the FRW cosmological model.

Findings

Establishes a link between Riccati and Korteweg-de Vries equations in cosmology

Shows embedding of discrete adiabatic indices in soliton solutions

Provides a mathematical framework for soliton behavior in cosmological models

Abstract

Applying standard mathematical methods, it is explicitly shown how the Riccati equation for the Hubble parameter H(\eta) of barotropic open FRW cosmologies is connected with a Korteweg-de Vries equation for adiabatic index solitons. It is also shown how one can embed a discrete sequence of adiabatic indices of the type n^2({3/2}\gamma -1)^2 (\gamma \neq 2/3) in the sech FRW adiabatic index soliton