On the analytical and numerical approximations to the forced damped Gardner Kawahara equation and modeling the nonlinear structures in a collisional plasma

Abstract

We perform a detailed study on the completely non-integrable forced damped Gardner/Extended Kawahara equation (FDEKE). Three techniques are introduced to determine abundance approximations to the proposed equation. In the first technique, the ansatz method is carried out for deriving some general formulas for the analytical approximations. In the second and third techniques, the FDEKE is analyzed numerically using both the septic B-spline collocation method and the method of lines. As a realistic model, the obtained approximations are employed for studying the properties of the periodic forced dissipative extended Kawahara solitary and cnoidal waves in a pair-ion plasma comprised of Maxwellian electrons and two fluid positive and negative ions. Both numerical and analytical approximations are graphically compared with each other. Also, the global maximum residual error L∞ for all obtained approximations is estimated for checking the accuracy of these approximations. Moreover, the obtained approximations can be applied for studying the features of the dissipative localized and periodic higher-order structures in optical fiber, ocean, sea, different models of plasma physics, and fluid mechanics.