  We show that hydrodynamic theories of polar active matter generically possess
inhomogeneous traveling solutions. We introduce a unifying dynamical-system
framework to establish the shape of these intrinsically nonlinear patterns, and
show that they correspond to those hitherto observed in experiments and
numerical simulations: periodic density waves, and solitonic bands, or
polar-liquid droplets both cruising in isotropic phases. We elucidate their
respective multiplicity and mutual relations, as well as their existence
domain.
