Novel exact soliton solutions for the extended (3+1)-dimensional Kairat –II equation using two robust techniques

Abstract

This research explores the extended (3+1)-dimensional Kairat–II equation by employing the logistic equation method and the modified Kudryashov approach. The Kairat family of equations is notable for capturing second-order spatiotemporal dispersion and group velocity dispersion, which are significant in the study of curve differential geometry and various equivalence relations. The extended form of the equation introduces three additional linear diffusion terms, enriching the physical phenomena already described by the original model. This work presents a range of solitary wave solutions, including their propagation patterns, by applying hyperbolic and trigonometric function-based solutions. These include multiple breather, kink, and other essential wave structures relevant to optical fiber technology, signal processing, and telecommunication systems. Additionally, 3D, 2D, contour and polar coordinate plots are provided to visually represent the analytical soliton dynamics within the extended Kairat equation. The obtained solutions offer new perspectives in fields such as optical communication, fiber optics, oceanography, and quantum mechanics.