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Ferroelectric materials, such as lithium niobate, show interesting nonlinear hysteresis behavior that can be explained by a dynamical system analysis by using a nonlinear Klein-Gordon equation previously constructed from the Hamiltonian with Landau-Ginzburg two-well potential. In the discrete case [Phys. Rev. B 81, 064104 (2010)], the intrinsic localized modes were shown to exist above the linear modes. Nonlinearity and discreteness of domain structures in ferroelectrics slab domains arrayed in the x-direction lead to breather solutions under different values of controlling parameters, such as interaction between the domains and damping term mainly due to pinning effect. Different types of classical breather solution, namely Hamiltonian, dissipative and moving breather solutions are shown by numerical simulation with data on actual ferroelectric materials.

In a previous dynamic study of some ferroelectric materials showing memory switching behavior, a Hamiltonian was developed that gave rise to a nonlinear Duffing oscillator equation involving the Landau-Ginzburg free energy functional as a potential formulation (Bandyopadhyay et al 2006 J. Appl. Phys. 100 114106). A high level of oscillations was observed in polarization waves against non-dimensional time that was quenched by increasing damping, which is a decay constant related to the loss of polarization due to damping during its motion in a ferroelectric material, such as lithium niobate. From the computer simulation of the damped oscillation curves, a critical time for switching, say, in a nanoswitch, was found that varies with the damping coefficient. This damping was also found to show an increasing behavior with the coercive field or the amount of impurities in a quadratic manner in such ferroelectrics.

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The dark and bright solitons in different systems are already known. If the intrinsic field is only considered, then the modal dynamics for small oscillations could be characterized by the bound state in a limited range of frequency, revealed via associated Legendre polynomial. The pairing and interplay between the dark and bright solitons occur. The disappearance of the bound state after a critical frequency gives rise to dark solitons in the unbound states that propagate through the domains. Above the upper boundary of the bound states, the estimated frequencies of dark solitons match with those experimentally found for ‘acoustical memory’.