Nonlinear sigma models solvable by the Aratyn-Ferreira-Zimerman ansatz

TL;DR

This paper explores nonlinear sigma models that are exactly solvable using the Aratyn-Ferreira-Zimerman ansatz, revealing models with knot solitons and connections to the fifth Painleve equation, depending on specific weight factors.

Contribution

It introduces new solvable nonlinear sigma models with variable weight factors, including one linked to the fifth Painleve equation, and discusses their soliton solutions.

Findings

Models with definite Hopf index configurations

Existence of knot solitons confined in finite volume

Connection to the fifth Painleve equation for specific weight factors

Abstract

Nonlinear sigma models compatible with the aratyn-Ferreira-Zimerman ansatz are discussed, the latter ansatz automatically leading to configurations with definite values of the Hopf index. These models are allowed to involve a weight factor which is a function of one of the toroidal coordinates. Depending on the choice of the weight factor, the field equation takes various forms. In one model with a special weight factor, the field equation turns out to be the fifth Painleve equation. This model suggests the existence of a knot soliton strictly confined in a finite spatial volume. Some other interesting cases are also discussed.