Solitonic solutions of Faddeev model

TL;DR

This paper explores solitonic solutions in the Faddeev model by reducing the static field equations to a nonlinear ODE and solving it numerically, linking solutions to topological invariants.

Contribution

It introduces a new approach to find solitonic solutions of the Faddeev model using a specific equation and numerical methods, connecting solutions to topological invariants.

Findings

Numerical solitonic solutions obtained for the Faddeev model.

Product of solution integers correlates with the Hopf invariant.

Reduction of field equations to a solvable nonlinear ODE.

Abstract

An application of the equation proposed by the present authors, which is equivalent to the static field equation of the Faddeev model, is discussed. Under some assumptions on the space and on the form of the solution, the field equation is reduced to a non-linear ODE of second order. By solving this equation numerically, some solitonic solutions are obtained. It is discussed that the product of two integers specifying solutions may be identified with the Hopf topological invariant.