Dark lump collision phenomena to a nonlinear evolution model in harmonic crystals

Abstract

In this paper, we examine the innovative KdV model, which has a profound impact on our understanding of a range of nonlinear occurrences of ion-acoustic waves in plasma and acoustic waves in harmonic crystals. Using the appropriate transformations, Hirota bilinearization is performed to generate the solutions. Using trigonometric, hyperbolic, and exponential functions, we generate collision aspects between lumps and other solutions in order to establish some more interaction solutions with some innovative physical characteristics. We obtain the two-wave, dark lump wave and lump-periodic solutions. The identified solutions are visually represented. In the fields of shallow-water waves, ion-acoustic waves in plasma, and acoustic waves in harmonic crystals, the current work is extensively exploited to describe a variety of remarkable physical events. To ensure the accuracy of the result, all the obtained solutions are placed in the model. © 2025 The Author(s)