Painlev{\'e} singularity structure analysis of three component Gross-Pitaevskii type equations

TL;DR

This paper investigates the integrability of a three-component Gross-Pitaevskii system using Painlevé analysis, identifying specific parameter sets where the system is integrable, thus contributing to understanding spinor Bose-Einstein condensates.

Contribution

The study applies Painlevé singularity analysis to a three-component Gross-Pitaevskii system, pinpointing the exact parametric conditions for integrability.

Findings

Only two parametric choices lead to integrability.

The system passes the Painlevé test only in known integrable cases.

Identifies conditions relevant for spinor Bose-Einstein condensates.

Abstract

In this paper, we have studied the integrability nature of a system of three coupled Gross-Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose-Einstein condensates by applying the Painlev\'e singularity structure analysis. We show that only for two sets of parametric choices, corresponding to the known integrable cases, the system passes the Painlev\'e test.