Dynamical behavior of synchronized symmetric waves in the two-mode Chaffee-Infante model via Hirota bilinear transformation - Muhammad Zafarullah Baber; Ebrima Bittaye; Hijaz Ahmad; Baboucarr Ceesay; Nauman Ahmed (Results in Engineering, 2025)
In this work, we study the dynamical behavior of synchronized propagation of two symmetric waves in an extended (1+1)-dimensional Chaffee-Infante (CI) framework, known as the two-mode Chaffee-Infante (TMCI) model. The Chaffee-Infante model is generalized to a second-order evolutionary partial differential equation incorporating the effects of dispersion, nonlinearity, and phase velocity. In order to build and compare exact solutions, the Hirota bilinear transformation technique is used, allowing for the systematic generation of a range of nonlinear wave forms, such as solitary waves, breathers, kinks, periodic lump waves, and mixed and multi wave configurations. Mathematica is used quite extensively to carry out the symbolic manipulations needed to acquire the solutions and to display resulting wave behavior with 3D surface plots, contour plots, and 2D profiles. The graphical representations unveil rich dynamical regimes, from stable solitary wave propagation to complex breather and soliton crystal structures, emphasizing the roles of synchronization, modulation, and phase interactions among the symmetric waves. This research presents a complete characterization of the synchronization phenomena in two-mode nonlinear systems and provides useful insights into coherent structure formation in dispersive and nonlinear media.