Exploring optical solutions of (3+1)-dimensional Kairat-X equation

The current research focuses on establishing an analytical approach to an equation that is very important in mathematics and physics. This model is known as the (3+1)-dimensional Kairat-X equation (K-XE), which describes the trajectory of optical pulses in optical fibers. This study presents solutions to the nonlinear (3+1)-dimensional Kairat-X equation (K-XE). Using four distinct approaches, we have found new exact trigonometric, hyperbolic and exponential solutions of the (3+1) dimensional Kairat-X equation (K-XE), which are not found in the literature. Using the computational program Maple, various solutions are presented in three dimensions to illustrate the physical phenomena of this model. This is done by assigning particular values to the constraint parameters. Therefore, our work’s inventiveness is demonstrated by the application of many types of new solutions and newly employed creative ways. This facilitates additional research into nonlinear models that realistically capture important physical processes in daily life. Up until now, these solutions to this equation have not been discovered in any literature.