A collaborative research effort involving a researcher Özşahin from Near East University introduces innovative methods for exact estimations of complex equations governing population dynamics and quantum field theory interactions. The study employs the Modified Extended Tanh-Function Method (METFM) and the Ricatti–Bernoulli Sub-ODE Method (RBSOM) to achieve precise solutions for the Zoomeron equation and the time-fraction biological population model (TFBPM).
Through meticulous implementation of METFM and RBSOM, the research team successfully establishes advanced and accurate wave solutions for the studied models. Figures 1–6 depict the exact solutions derived using METFM, while Figures 7–10 showcase solutions obtained through RBSOM. These solutions encompass a variety of functions, including trigonometric and hyperbolic functions, periodic soliton solutions, and rational solitons, providing new insights into population dynamics and quantum field theory.
The findings not only enhance our understanding of population distribution dynamics and quantum field interactions but also have practical implications for various fields, including demographic modeling and quantum electrodynamics. The newly established solutions inspire positive motivation for societal balance and international harmony, contributing to global peace and cooperation.
Furthermore, the introduction of RBSOM as a novel technique demonstrates the research team’s commitment to exploring innovative methods for addressing complex problems where traditional approaches may falter. The method enables the identification of infinite series of solitary solutions through Bäcklund transformation, expanding the scope of solutions achievable for intricate equations.
The research effort yields groundbreaking results, advancing the field of mathematical modeling and offering valuable insights into population dynamics and quantum field theory interactions. The precise solutions obtained through METFM and RBSOM hold promise for addressing real-world challenges and fostering societal harmony on both local and global scales.
More Information:
https://www.degruyter.com/document/doi/10.1515/phys-2022-0252/html
