  Nonlinear and low-frequency solitary waves are investigated in the framework
of the one-dimensional Hall-magnetohydrodynamic model with finite Larmor
effects and a double adiabatic model for plasma pressures. The organization of
these localized structures in terms of the propagation angle with respect to
the ambient magnetic field $\theta$ and the propagation velocity $C$ is
discussed. There are three types of regions in the $\theta-C$ plane that
correspond to domains where either solitary waves cannot exist, are organized
in branches, or have a continuous spectrum. A numerical method valid for the
two latter cases, that rigorously proves the existence of the waves, is
presented and used to locate many waves, including bright and dark structures.
Some of them belong to parametric domains where solitary waves were not found
in previous works. The stability of the structures has been investigated by
first performing a linear analysis of the background plasma state and second by
means of numerical simulations. They show that the cores of some waves can be
robust but, for the parameters considered in the analysis, the tails are
unstable. The substitution of the double adiabatic model by evolution equations
for the plasma pressures appears to suppress the instability in some cases and
to allow the propagation of the solitary waves during long times.
