This paper deals with solutions to the \(U(1)\) complex scalar Higgs equations in 1 + 2 dimensions, regarded as models for tube-like solutions in three space dimensions. The equations are nonlinear hyperbolic and few non-trivial exact solutions are known. This paper deals with approximation techniques for investigating the moduli space of a class of solutions known as vortices, which display certain particle-like behavior and motion. The kinetic energy induces a Kähler metric on the moduli space, and vortex motion is approximately geodesic. In particular, the vortex-vortex scattering problem is studied in some numerical detail.