  We study soliton solutions in scalar field theory with a variety of unbounded
potentials. A subset of these potentials have Gaussian lump solutions and their
fluctuation spectrum is governed by the harmonic oscillator problem. These
lumps are unstable with one tachyonic mode. Soliton solutions in several other
classes of potentials are stable and are of kink type. The problem of the
stability of these solutions is related to a supersymmetric quantum mechanics
problem. The fluctuation spectrum is not equispaced and does not contain any
tachyonic mode. The lowest energy mode is the massless Goldstone mode which
restores broken translation invariance.
