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The paper deals with a theoretical model for interacting dark energy. Theinteraction between the cold dark matter (dust) and the dark energy has beenassumed to be non-gravitational in nature. Exact analytic cosmologicalsolutions are obtained both for constant and variable equation of state fordark energy. It is found that, for very small value of the coupling parameter(in the interaction term), the model asymptotically extends up to $\Lambda$CDM,while the model can enter into the phantom domain asymptotically, if thecoupling parameter is not so small. Both the solutions are then analyzed with194 Supernovae Type Ia data. The best fit parameters are shown with 1$\sigma$and 2$\sigma$ confidence intervals. Finally, we have discussed the cosmographicparameters for both the cases.

An analytic model for interacting dark energy and its observational constraints