Dark energy cosmological models with cosmic string

In this paper we have studied the anisotropic Kantowski-Sachs, locally rotationally symmetric (LRS) Bianchi type-I and LRS Bianchi type-III geometries filled with dark energy and one dimensional cosmic string in the Saez-Ballester theory of gravitation. To get physically valid solution we take hybrid expansion law of the average scale factor which is a product of power and exponential type of functions that results in time dependent deceleration parameter (). The equation of state parameter of dark energy () has been discussed and we have observed that for the three models it crosses the phantom divide line () and shows quintom like behavior. The density of dark energy () is an increasing function of redshift and remains positive throughout the evolution of the universe for the three models. Moreover in Kantowski-Sachs and LRS Bianchi type-I geometries the dark energy density dominates the string tension density () and proper density () throughout the evolution of the universe. The physical and geometrical aspects of the statefinder parameters (), squared speed of sound () and - plane are also discussed.