  We present experimental and theoretical evidence of novel bound state
formation in the low transverse field ordered phase of the
quasi-one-dimensional Ising-like material CoNb$_2$O$_6$. High resolution single
crystal inelastic neutron scattering measurements observe that small transverse
fields lead to a breakup of the spectrum into three parts, each evolving very
differently upon increasing field. This can be naturally understood starting
from the excitations of the ordered phase of the transverse field Ising model,
domain wall quasiparticles (solitons). Here, the transverse field and a
staggered off-diagonal exchange create one-soliton hopping terms with opposite
signs. We show that this leads to a rich spectrum and a special field, when the
strengths of the off-diagonal exchange and transverse field match, at which
solitons become localized; the highest field investigated is very close to this
special regime. We solve this case analytically and find three two-soliton
continua, along with three novel bound states. Perturbing away from this novel
localized limit, we find very good qualitative agreement with the experimental
data. We also present calculations using exact diagonalization of a recently
refined Hamiltonian model for CoNb$_2$O$_6$ and using diagonalization of the
two-soliton subspace, both of which provide a quantitative agreement with the
observed spectrum. The theoretical models qualitatively and quantitatively
capture a variety of non-trivial features in the observed spectrum, providing
insight into the underlying physics of bound state formation.
