Considering the general Lagrangian of k-essence models , we study and classify them through variables connected to the fluid equation of state parameter w _ { \kappa } .
This allows to find solutions around which the scalar field describes a mixture of dark matter and cosmological constant-like dark energy , an example being the purely kinetic model proposed by Scherrer .
Making the stronger assumption that the scalar field Lagrangian is exactly constant along solutions of the equation of motion , we find a general class of k-essence models whose classical trajectories directly describe a unified dark matter/dark energy ( cosmological constant ) fluid .
While the simplest case of a scalar field with canonical kinetic term unavoidably leads to an effective sound speed c _ { s } = 1 , thereby inhibiting the growth of matter inhomogeneities , more general non-canonical k-essence models allow for the possibility that c _ { s } \ll 1 whenever matter dominates .