  A lagrangian for the $k-$ essence field is set up with canonical kinetic
terms and incorporating the scaling relation of [1]. There are two degrees of
freedom, {\it viz.},$q(t)= ln\enskip a(t)$ ($a(t)$ is the scale factor) and the
scalar field $\phi$, and an interaction term involving $\phi$ and $q(t)$.The
Euler-Lagrange equations are solved for $q$ and $\phi$. Using these solutions
quantities of cosmological interest are determined. The energy density $\rho$
has a constant component which we identify as dark energy and a component
behaving as $a^{-3}$ which we call dark matter. The pressure $p$ is {\it
negative} for time $t\to \infty$ and the sound velocity $c_{s}^{2}={\partial
p\over\partial\rho} << 1$. When dark energy dominates, the deceleration
parameter $Q\to -1$ while in the matter dominated era $Q\sim {1\over 2}$. The
equation of state parameter $w={p\over \rho}$ is shown to be consistent with
$w={p\over\rho}\sim -1$ for dark energy domination and during the matter
dominated era we have $w\sim 0$. Bounds for the parameters of the theory are
estimated from observational data.
  Keywords: k-essence models, dark matter, dark energy
  PACS No: 98.80.-k
