Bifurcation Analysis and Soliton Behavior of New Combined Kairat-II-X Differential Equation Using Analytical Methods

The exact analytical solutions of a new combined Kairat-II-X differential equation are presented. The related model is investigated by combining the enhanced modified extended tanh function method and the modified tan(ϕ/2)-expansion method. Then, a wide range of solitary wave solutions with unknown coefficients are extracted in a variety of shapes, including dark, bright, bell-shaped, kink-type, combine, and complex solitons, exponential, hyperbolic, and trigonometric function solutions. To offer physical insight, some of the identified solutions are presented in figures. Also, 3D, 2D, and 2D density profiles of the obtained outcomes are illustrated in order to examine their dynamics with the choices of parameters involved. Based on the obtained findings, we can assert that the suggested computational approaches are efficient, dynamic, well-structured, and valuable for tackling complex nonlinear problems in several fields, including symbolic computations. The bifurcation analysis and sensitivity analysis are employed to comprehend the dynamical system. We assume that our findings will be very beneficial in improving our understanding of the waves that manifest in solids.