An exotic k-essence interpretation of interactive cosmological models

We define a generalization of scalar fields with non-canonical kinetic term which we call exotic k-essence or briefly, exotik. These fields are generated by the global description of cosmological models with two interactive fluids in the dark sector and under certain conditions, they correspond to usual k-essences. The formalism is applied to the cases of constant potential and of inverse square potential and also we develop the purely exotik version for the modified holographic Ricci type of dark energy (MHR), where the equations of state are not constant. With the kinetic function $F=1+mx$ and the inverse square potential we recover, through the interaction term, the identification between k-essences and quintessences of exponential potential, already known for Friedmann-Robertson-Walker and Bianchi type I geometries. Worked examples are shown that include the self-interacting MHR and also models with crossing of the phantom divide line (PDL).