The paper "On optical soliton wave solutions of non-linear Kairat-X equation via new extended direct algebraic method" by Ghulam Hussain Tipu et al. explores the use of the modified extended direct algebraic method to derive optical soliton solutions for the non-linear Kairat-X (K-X) equation. This equation models the propagation of optical solitons through nonlinear media, considering second-order spatiotemporal dispersion and group velocity dispersion. The study yields various types of soliton solutions, including bright, dark, and singular solitons, as well as periodic and exponential solutions. The authors generate 2D, 3D, and contour graphs to visualize the propagation of these solitons, providing a precise representation of physical phenomena. This research contributes to the advancement of understanding optical solitons and their behavior in nonlinear optical systems, particularly in telecommunications and signal processing. The paper also highlights the importance of non-linear partial differential equations (PDEs) in various scientific fields and the role of advanced computational methods in exploring these equations.The paper "On optical soliton wave solutions of non-linear Kairat-X equation via new extended direct algebraic method" by Ghulam Hussain Tipu et al. explores the use of the modified extended direct algebraic method to derive optical soliton solutions for the non-linear Kairat-X (K-X) equation. This equation models the propagation of optical solitons through nonlinear media, considering second-order spatiotemporal dispersion and group velocity dispersion. The study yields various types of soliton solutions, including bright, dark, and singular solitons, as well as periodic and exponential solutions. The authors generate 2D, 3D, and contour graphs to visualize the propagation of these solitons, providing a precise representation of physical phenomena. This research contributes to the advancement of understanding optical solitons and their behavior in nonlinear optical systems, particularly in telecommunications and signal processing. The paper also highlights the importance of non-linear partial differential equations (PDEs) in various scientific fields and the role of advanced computational methods in exploring these equations.