Integrable Zhaidary equations: reductions and gauge equivalence

TL;DR

This paper investigates the integrability of generalized spin systems in 1+1 dimensions, providing Lax representations, gauge equivalences, and connections to Zhanbota equations and Painleve equations.

Contribution

It introduces new Lax representations and establishes gauge equivalences between Zhanbota equations and Painleve equations, advancing the understanding of integrable systems.

Findings

Lax representations for generalized spin systems derived

Gauge equivalences between ISS and Zhanbota equations established

Connections between Zhanbota equations and Painleve equations demonstrated

Abstract

The present work addresses the study and characterization of the integrability of some generalized spin systems (ISS) in 1+1 dimensions. Lax representations for these ISS are successfully obtained. The gauge equivalent counterparts of these integrable ISS are presented. Finally, we consider Zhanbota transcendents and some integrable Zhanbota equations. In particular, the gauge equivalence between some Zhanbota equations and the six Painleve equations is established.