Below Curie temperature, certain perovskites show important ferroelectric behaviour, which have a wide range of applications, notably in non-linear photonic devices and as non-volatile memory. Previously, a Klein-Gordon (KG) equation has been derived based on a discrete Hamiltonian. On a multiple time scale analysis (MTSA), based on discrete polarization domains, intrinsic localized modes (ILM) were observed [1], which are nonlinear excitations that are produced by the nonlinearity and discreteness of the lattice. These are highly localized pulses in space that are found in the discrete nonlinear model formulation. As the continuum limit formulation cannot be applied to their study, the present formulation is appropriate to highly localized pulses having widths that are not large compared to the domain widths. This question about the appropriate length scale drives us to nano-range of domain walls in ferroelectrics [2] having many interesting applications in nanostructured arrays of sensors, actuators, etc.
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