Tri-analytical approach to Kairat-II and Kairat-X equations

The Kairat-II equation and the Kairat-X equation are two nonlinear partial differential equations (PDEs) that have been studied extensively in recent years. The origin of these equations is attributed to the work of Kairat, a researcher who developed these equations to describe various physical phenomena, such as the behavior of optical pulses in optical fibers and plasma physics. The study employs three robust analytical techniques: the ( G0 G ), the Bernoulli Sub-ODE, and the modified auxiliary equation (MAE) methods. Each method contributes uniquely to obtaining exact solutions, offering valuable insights into solving nonlinear differential equations effectively. Finally, to further highlight our findings, we provide a few two- and three-dimensional plots.