We propose to use dynamical symmetries of the field equations, in order toclassify the dark energy models in the context of scalar field (quintessence orphantom) FLRW cosmologies. Practically, symmetries provide a usefulmathematical tool in physical problems since they can be used to simplify agiven system of differential equations as well as to determine theintegrability of the physical system. The requirement that the field equationsadmit dynamical symmetries results in two potentials one of which is the wellknown Unified Dark Matter (UDM) potential and another new potential. For eachhyperbolic potential we obtain the corresponding analytic solution of the fieldequations. The proposed analysis suggests that the requirement of the contactsymmetry appears to be very competitive to other independent tests used toprobe the functional form of a given potential and thus the associated natureof dark energy. Finally, in order to test the viability of the above scalarfield models we perform a joint likelihood analysis using some of the latestcosmological data.
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