We found the exact solution for a model consisting of two dipole-coupled qubits, one of which is an isolated, and the other interacts with the thermal mode of a cavity with the Kerr medium. The results showed that Kerr nonlinearity may greatly enhance the degree of entanglement induced by a thermal field both for separable and entangled initial states of qubits. We also showed the possibility of the disappearance of the sudden death of entanglement for a model with a Kerr nonlinearity..
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