  A unified formulation that obtains solitary waves for various background
densities in the Bose-Einstein condensate of a system of hard-core bosons with
nearest neighbor attractive interactions is presented.
  In general, two species of solitons appear: A nonpersistent (NP) type that
fully delocalizes at its maximum speed, and a persistent (P) type that survives
even at its maximum speed, and transforms into a periodic train of solitons
above this speed. When the background condensate density is nonzero, both
species coexist, the soliton is associated with a constant intrinsic frequency,
and its maximum speed is the speed of sound. In contrast, when the background
condensate density is zero, the system has neither a fixed frequency, nor a
speed of sound. Here, the maximum soliton speed depends on the frequency, which
can be tuned to lead to a cross-over between the NP-type and the P-type at a
certain critical frequency, determined by the energy parameters of the system.
We provide a single functional form for the soliton profile, from which diverse
characteristics for various background densities can be obtained. Using the
mapping to spin systems enables us to characterize the corresponding class of
magnetic solitons in
  Heisenberg spin chains with different types of anisotropy, in a unified
fashion.
