Wave structures, modulation instability analysis and chaotic behaviors to Kudryashov’s equation with third-order dispersion

This research aims to conduct a comprehensive qualitative and quantitative analysis of Kudryashov’s equation with third-order dispersion. Initially, the equation is converted into a two-dimensional dynamic system through the application of the traveling wave transformation. The generalized trial equation method is then utilized to derive Gaussian soliton solutions. Furthermore, the existence of periodic and soliton solutions in the equation is established by utilizing the burification method. The conclusions of the theoretical analysis are validated by constructing exact solutions, and the modulation instability of the equation is also explored. Moreover, by introducing various perturbation terms, we investigate the chaotic properties of the equations under different perturbation terms. This research represents the first thorough investigation of all possible traveling wave solutions for Kudryashov’s equation with third-order dispersion, and also uncovers notable chaotic behavior under specific perturbation scenarios.