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We consider a variant of the standard electroweak theory in which the Higgssector has been modified so that there is a classically stable weak scalesoliton. We explore fermion number violating processes which involve solitondecay. A soliton can decay by tunnelling under the sphaleron barrier, or thedecay can be collision induced if the energy is sufficient for the barrier tobe traversed. We present a classical solution to the Minkowski space equationsof motion in which a soliton is kicked over the barrier by an incoming pulse.This pulse corresponds to a quantum coherent state with mean number of $W$quanta $\sim 2.5/g^2$ where $g$ is the $SU(2)$ gauge coupling constant. We alsogive a self-contained treatment of the relationship between classicalsolutions, including those in which solitons are destroyed, and tree-levelquantum amplitudes. Furthermore, we consider a limit in which we can reliablyestimate the amplitude for soliton decay induced by collision with a single$W$-boson. This amplitude depends on $g$ like $\exp (-cg^{-1/3})$, and islarger than that for spontaneous decay via tunnelling in the same limit.Finally we show that in soliton decays, light $SU(2)_L$ doublet fermions areanomalously produced. Thus we have a calculation of a two body process withenergy above the sphaleron barrier in which fermion number is violated.Comment: 64 pages, revtex, epsf, all figures included. Revised version.  Section V replaced with a corrected version. Qualitative conclusions  unchanged. Numerical value of one exponent has change

Collision-induced decays of electroweak solitons: Fermion number violation with two and few initial particles