New solitary wave solutions for two (3+1)-dimensional extended Kairat-type equations via the generalized Riccati equation method

This paper investigates various soliton solutions for the newly introduced extended [Formula: see text]-dimensional Kairat-II and Kairat-X equations using the improved generalized Riccati equation method. Kairat equations are known due to their involvement with second-order spatiotemporal dispersion and group velocity dispersion, which illustrate curve differential geometry, and many equivalence relations. The extension of these equations contains three additional linear diffusion terms to the existing physical phenomena that already exist in these equations. This study proposes different solitary wave solutions and their propagation using various hyperbolic and trigonometric function solutions in the forms of multiple, breather, kink and other important wave structures in optical fibers, signal processing, and telecommunication systems. Furthermore, we provided 2D, 3D, and contour plots to showcase the representations of the analytic physical solitons phenomena in the extended Kairat equations. The derived solutions will unlock new insights into optical communication, optical fiber, oceanography, and quantum mechanics.