On optical soliton wave solutions of non-linear Kairat-X equation via new extended direct algebraic method

The optical soliton is a hot topic in studying. In the current research, we utilize the modified extended direct algebraic method to derive optical soliton solutions for the non-linear Kairat-X (K-X) equation, which considers second-order spatiotemporal dispersion and the group velocity dispersion. The significant Kairat-X equation is considered to develop the soliton solutions because, Solitons are valuable because they are stable, retain their shape during propagation, and have applications ranging from telecommunications and signal processing to quantum physics and materials science. This equation describe how optical solitons propagate through non-linear media. Prior to this study, there was no existing research in which such solutions could be found. Our research yields various types of soliton solutions, including bright, dark, and singular solitons, as well as periodic and exponential solutions. Under specific parameters, we generate 2D, 3D, and contour graphs to visualize the propagation of optical soliton, allowing us to showcase its precise representation of physical phenomena. This work contributes to the advancement of our understanding of optical solitons and their behavior in non-linear optical systems.