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A model of phase transitions with coupling between the order parameter andits gradient is proposed. It is shown, that this nonlinear model is suitablefor the description of phase transitions accompanied by the formation ofspatially inhomogeneous distributions of the order parameter. Exact solutionsof the proposed model are obtained for the special cases which can be relatedto the spinodal decomposition or cosmological scenario. The proposed model isanalogical to the mechanical nonlinear oscillator with the coordinate-dependentmass or velocity dependent elastic module. Based on this analogy, the existenceof the limit cycles is established.

A model of phase transitions with coupling between the order parameter and its gradient