Dynamics of CP1 lumps on a cylinder

The slow dynamics of topological solitons in the CP1σ -model, known as lumps, can be approximated by the geodesic flow of the L2 metric on certain moduli spaces of holomorphic maps. In the present work, we consider the dynamics of lumps on an infinite flat cylinder, and we show that in this case the approximation can be formulated naturally in terms of regular Kähler metrics. We prove that these metrics are incomplete exactly in the multilump (interacting) case. The metric for two-lumps can be computed in closed form on certain totally geodesic submanifolds using elliptic integrals; particular geodesics are determined and discussed in terms of the dynamics of interacting lumps.