Multisoliton solutions for equivariant wave maps on a 2+1 dimensional wormhole

We study equivariant wave maps from the 2+1 dimensional wormhole to the 2-sphere. This model has explicit harmonic map solutions which, in suitable coordinates, have the form of the sine-Gordon kinks/antikinks. We conjecture that there exist asymptotically static chains of N≥2 alternating kinks and antikinks whose subsequent rates of expansion increase in geometric progression as t→∞. Our argument employs the method of collective coordinates to derive effective finite-dimensional ODE models for the asymptotic dynamics of N-chains. For N=2, 3 the predictions of these effective models are verified by direct PDE computations which demonstrate that the N-chains lie at the threshold of kink-antikink annihilation.