On the stable computational, semi-analytical, and numerical solutions of the Langmuir waves in an ionized plasma

This research paper investigates the stable computational, semi-analytical, and numerical solutions of the nonlinear complex fractional generalized-Zakharov system. This system describes the nonlinear interactions between the low-frequency, acoustic waves and high-frequency, electromagnetic waves. The modified Khater method is applied to find the analytical solutions then the stability property of these solutions is discussed by using the Hamiltonian system properties. Moreover, stable computational solutions are used as the initial condition in the semi-analytical and numerical schemes. The Adomian decomposition and septic B-spline schemes are used to find the semi-analytical and numerical. For more explanation of the obtained analytical solutions, some sketched are plotted in different types. Also, the comparison between the distinct types of obtained solutions is shown by calculating the absolute value of error. The performance of the used method explains the powerful, effective, and the ability for applying to different forms of nonlinear evolution equation.