  This paper studies traveling waves with nonzero wave speed (angular traveling
waves) of the high-dimensional Boussinesq equation that have not been studied
before. We analyze the properties of these waves and demonstrate that, unlike
the unique stationary solution, they lack positivity, radial symmetry, and
exponential decay. By employing variational and geometric approaches, along
with perturbation theory, we establish the orbital (in)stability and strong
instability of these traveling waves.
