  We investigate some new similarity inhomogeneous solutions of anisotropic
dark energy and perfect fluid in Bianchi type-I space-time. Three different
equation of state parameters along the spatial directions are introduced to
quantify the deviation of pressure from isotropy. We consider the case when the
dark energy is minimally coupled to the perfect fluid as well as direct
interaction with it. The Lie symmetry generators that leave the equation
invariant are identified and we generate an optimal system of one-dimensional
subalgebras. Each element of the optimal system is used to reduce the partial
differential equation to an ordinary differential equation which is further
analyzed. We solve the Einstein field equations, described by a system of
non-linear partial differential equations (NLPDEs), by using the Lie point
symmetry analysis method. The geometrical and kinematical features of the
models and the behavior of the anisotropy of dark energy, are examined in
detail.
