Analytical Study of the Generalized Kudryashovs Model through the New Mapping Method with Physical Interpretation

Abstract

The generalised Kudryashov equation, a nonlinear evolution equation that accurately simulates the propagation of ultra-short pulses in dispersive and nonlinear media, is analytically investigated in this study. A recently created generalised mapping approach is used to solve this equation. The suggested approach is more adaptable and independent of constrictive assumptions than traditional methods, which enables the derivation of a larger class of exact answers. A wide variety of soliton forms, such as W-shaped, dark, sharp, kink, peakon, bell, smooth, and anti-bell solitons, are produced using this technique. Every solution provides insightful interpretations in a range of physical circumstances and exhibits unique nonlinear behaviours impacted by the model's parameters. These solitons are important because they represent localised energy packets, intensity dips, or transitional wavefronts in domains like fluid mechanics, wave propagation, nonlinear optics, and plasma physics. The effectiveness and dependability of the novel mapping method are confirmed by the results' graphical representation, which demonstrates the generalised Kudryashov model's ability to accommodate a broad range of waveforms. Such soliton profiles' appearance highlights the model's capacity to accurately predict intricate nonlinear processes. The study offers a clearer understanding of the rich structure of nonlinear wave events governed by higher-order dispersion and nonlinearity, in addition to improving the analytical solution space of the generalised Kudryashov equation. Combining the advanced model with the proposed mapping technique creates a robust analytical framework for studying nonlinear systems in mathematical physics and applied sciences.