Energy Transfer and Interaction Mechanism of Kink‐Antikink Waves in Nonlinear Media

ABSTRACT Nonlinear wave equations have attracted broad interest due to their numerous applications in physics, engineering, and applied mathematics. Kink‐antikink interactions are a key phenomenon in nonlinear dynamics, providing insights into energy transfer, soliton collisions, and wave propagation in dispersive and nonlinear media. This study examines kink‐antikink interactions in the and models utilizing collective coordinates and computational methods. Here, and represent models of scalar fields which are influenced by fourth‐ and sixth‐order nonlinear potentials, respectively. The model has two degenerate vacuum states, while the model has three vacuum states. The presence of three vacuum states creates more intricate structures and interaction mechanisms for kink and antikink pairs. With the help of bilinear transformations and ansatz‐based analytical methods, we construct and study the nonlinear wave solutions and their interactions in the and Klein‐Gordon models. Using advanced mathematical approaches, we investigate a variety of tactics, including periodic waves, periodic cross‐kink waves, periodic cross‐lump waves, lump waves, and configurations with single or many kinks. In addition, we investigate various interactions such as kink‐cross[SR1]‐rational solutions, periodic cross‐rational kinks, homoclinic breather solutions, and M‐shaped rational solutions of varied complexity. The structure and dynamics of these intricate waves are shown through multidimensional graphical representations, which enhance understanding of models' nonlinear waves.