Abstract
We introduce an unusual asymmetric double well potential, a piecewise parabolic one, and we show that the solutions for the evolution of its domain walls can be found analytically, in contrast with the case of the standard ${\ensuremath{\varphi}}^{4}$ field theory. We find exact solutions for the critical bubble, for the motion of domain walls in one, two and three spatial dimensions, and for the Euclidean O(4) bounce that determines the decay rate of the false vacuum.
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