Exploration of soliton solutions and chaos analysis in thin-film ferroelectric materials.

This research comprehensively examines the Thin-Film Ferroelectric Material Equation (TFFEME). TFFEME is vital in ferroelectric materials, offering a theoretical means to understand and predict ferroelectric thin-film behavior. These films are applied in non-volatile memories, sensors, and actuators, and TFFEME aids in accurately depicting internal physical processes for device performance optimization. By applying the beta fractional derivative with the modified (G'G2)-expansion method, diverse soliton solutions were derived. This not only broadens our understanding of TFFEME's solution framework but also provides insights into polarization dynamics and chaos analysis in ferroelectric thin films, applicable for enhancing ferroelectric-based device performance, like faster switching and lower power in non-volatile memories. The study also explored how physical parameters and fractional derivative forms affect solutions, crucial for soliton propagation. This analysis serves as a basis for improving material properties and innovating device designs, such as enhancing sensor sensitivity. Moreover, TFFEME was transformed into a Hamiltonian structure to study its planar dynamics, which is essential for predicting the device long-term stability. Finally, the barycentric Lagrange interpolation method at Chebyshev nodes provided precise numerical solutions for TFFEME, validating models and guiding experiments for new ferroelectric thin-film applications.