Approximate vortex solution of Faddeev model

Understand

Through an Ansatz specifying the azimuthal-angle dependence of the solution, the static field equation for vortex of the Faddeev model is converted to an algebraic ordinary differential equation.

• An approximate analytic expression of the vortex solution is explored so that the energy per unit vortex length becomes as small as possible.
• It is observed that the minimum energy of vortex is approximately proportional to the integer which specifies the solution.