A generalized trial equation scheme: A tool for solving thin films constructed from the ferroelectric materials

Abstract

In this paper, the thin-film ferroelectric material equation (TFFME) which enables the propagation of solitary polarization in thin-film ferroelectric materials is investigated, and also illustrated through the nonlinear evolution equations. Ferroelectrics are dielectric materials that exhibit nonlinear behaviors in wave propagation. Thin films constructed from the ferroelectric materials are utilized in different modern electronic devices. To investigate the characteristics of new waves, the solitary wave dynamics of the mentioned equation is used in the generalized trial equation scheme. The bright and periodic solutions are obtained by semi-inverse variational principle scheme. Many alternative responses may be obtained through different formulae; each of these solutions offers a distinct graph. The validity of such methods and solutions may be demonstrated by assessing how well the relevant techniques and solutions match up. The effects of free variables on the behavior of few achieved solutions for nonlinear rational exact cases are also plotted and explored depending upon the nature of nonlinearities. The dynamic properties of the obtained results are shown and analyzed by some density, two- and three-dimensional images. The results provide a way for future research on generating optical memories based on the nonlinear solitons.