Investigation the stability and novel explicit rational form solutions for two generalized nonlinear models: Kairat-II and Kairat-X equations

Abstract

Two upgrades of the Kairat equations, known as Kairat-II and Kairat-X, are examined in this research. The dynamics of wave propagation in nonlinear media, like optical fiber networks and shallow water settings, are taken into account by these two models. In order to address a variety of physical application implementations and provide future developments, we present these models with arbitrary coefficients. In order to derive explicit wave solutions using rational function approaches incorporating sine-cosine and sinh-cosh terms, an analytical methodology is enforced. The obtained solutions are described as having various wave shapes, including singular kink-wave, kink-wave, and periodic like-kink waves. Additionally, the Lyapunov direct technique is used to examine the stability of the derived solutions. We think that the results of this work provide important insights into the dynamics of wave behavior in nonlinear dispersive systems, in addition to shedding light on the Kairat-type equations.