  We study the dynamics of the quasi-one-dimensional Ising-Heisenberg
antiferromagnet BaCo2V2O8 under a transverse magnetic field. Combining
inelastic neutron scattering experiments and theoretical analyses by field
theories and numerical simulations, we mainly elucidate the structure of the
spin excitation spectrum in the high field phase, appearing above the quantum
phase transition point mu0Hc ~ 10 T. We find that it is characterized by
collective solitonic excitations superimposed on a continuum. These solitons
are strongly bound in pairs due to the effective staggered field induced by the
nondiagonal g tensor of the compound, and are topologically different from the
fractionalized spinons in the weak field region. The dynamical susceptibility
numerically calculated with the infinite time-evolving block decimation method
shows an excellent agreement with the measured spectra, which enables us to
identify the dispersion branches with elementary excitations. The lowest energy
dispersion has an incommensurate nature and has a local minimum at an
irrational wave number due to the applied transverse field.
