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 ($q$). The equation of state parameter of dark energy (${\omega }_{de}$) has been discussed and we have observed that for the three models it crosses the phantom divide line (${\omega }_{de}=-1$) and shows quintom like behavior. The density of dark energy (${\rho }_{de}$) 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 ($\lambda$) and proper density ($\rho$) throughout the evolution of the universe. The physical and geometrical aspects of the statefinder parameters ($r,s$), squared speed of sound ($v_s^2$) and ${\omega }_{de}$–${\omega }_{de}^{\prime }$ plane are also discussed.