On some novel lump interactions and soliton structures for the KdV-CDG model in fluids

This study investigates the Korteweg-de Vries-Caudrey-Dodd-Gibbon (KdV-CDG) equation, a significant nonlinear dynamical model that arises in fluid mechanics, ocean wave propagation, and plasma physics. Understanding exact wave structures of this model is important for describing nonlinear dispersive phenomena in these physical systems. To achieve this, the Hirota bilinear method is first employed to derive the bilinear form of the governing equation. Furthermore, the modified extended tanh-function method and the improved F-expansion approach are utilized to construct a broad class of analytical traveling wave solutions. The obtained results include diverse wave structures such as periodic wave solitons, lump solutions, lump–stripe interactions, and lump–periodic wave interactions. In addition, a wide variety of exact solutions—namely bright, rational, hyperbolic, trigonometric, periodic, W-shaped, and singular bell-shaped solitons are reported. Stability and modulation instability analyses are also performed, revealing that the derived traveling wave solutions exhibit stable behavior under the considered conditions. The physical characteristics of these solutions are further illustrated through two dimensional, contour, and three dimensional visualizations. The novelty of this work lies in the construction of new interaction solutions, particularly lump stripe and lump periodic wave structures, along with the simultaneous application of multiple analytical techniques to the considered model. These results extend existing studies in the literature and provide a deeper understanding of complex nonlinear wave dynamics, offering potential applicability to other higher-dimensional nonlinear evolution equations.