  We present the results of lattice computations of collisions of two expanding
bubbles of true vacuum in the Abelian Higgs model with a first-order phase
transition. New time-dependent analytical solutions for the Abelian field
strength and the phase of the complex field are derived from initial conditions
inferred from linear superposition and are shown to be in excellent agreement
with the numerical solutions especially for the case where the initial phase
difference between the bubbles is small. With a step-function approximation for
the initial phase of the complex field, solutions for the Abelian field
strength and other gauge-invariant quantities are obtained in closed form.
Possible extensions of the solution to the case of the electroweak phase
transition and the generation of primordial magnetic fields are briefly
discussed.
