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

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.

19 pages. Two column style is changed to preprint style

References in corpus (1)

• Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers

Cited by in corpus (2)

• Exact knot solutions in a generalized Skyrme-Faddeev model
• Skyrme-Faddeev Lagrangian from reformulated Georgi-Glashow model