Quintessence as k-essence
  Quintessence and k-essence have been proposed as candidates for the dark energy component of the universe that would be responsible of the currently observed accelerated expansion. In this paper we investigate the degree of resemblance between those two theoretical setups, and find that every quintessence model can be viewed as a k-essence model generated by a kinetic linear function. In addition, we show the true effects of k-essence begin at second order in the expansion of the kinetic function in powers of the kinetic energy. 
Juan M. Aguirregabiria, Luis P. Chimento, and Ruth Lazkoz