Parametrization of K-essence and Its Kinetic Term
  We construct the non-canonical kinetic term of a k-essence field directly from the effective equation of state function $w_k(z)$, which describes the properties of the dark energy. Adopting the usual parametrizations of equation of state we numerically reproduce the shape of the non-canonical kinetic term and discuss some features of the constructed form of k-essence. 
Hui Li, Zong-Kuan Guo and Yuan-Zhong Zhang