  We present an exact three-dimensional solitonic solution to a
sine-Gordon-type Euler-Lagrange equation, that describes a configuration of a
three-dimensional vector field n constrained to a surface p-vortex, with a
prescribed polar tilt angle on a planar substrate and escaping into the third
dimension in the bulk. The solution is relevant to characterization of a
schlieren texture in nematic liquid-crystal films with tangential (in-plane)
substrate alignment. The solution is identical to a section of a point defect
discovered many years ago by Saupe [Mol. Cryst. Liq. Cryst. 21, 211 (1973)],
when latter is restricted to a surface.

Soft Condensed Matter