EXPONENTIAL TIME DIFFERENCING SCHEME FOR MODELING THE DISSIPATIVE KAWAHARA SOLITONS IN A TWO-ELECTRONS COLLISIONAL PLASMA

In this work, a high efficiency and stable numerical method, which is called exponential time differencing fourth-order Runge-Kutta (EDT4RK) method, is introduced for the investigation of strong nonlinear and dispersive integrable and non-integrable differential equations. This method is applied for studying higher-order nonlinear structures that arise and propagate in plasma. The fluid equations of a plasma consisting of two electrons with different temperatures and immobile positive ions are reduced to a damped Kawahara equation via the reductive perturbation method. The damping term in the evolution equation appears due to taking the effect of electron-ion collision into account. If the damping term is ignored, the evolution equation reduces to the integrable Kawahara equation. The last equation has a hierarchy of exact solutions such as solitons and cnoidal waves. For modeling the dissipative solitons in the present plasma model, the numerical solution to the damped Kawahara equation is obtained via operating the EDT4RK method. The influence of the physical parameters related to the model under consideration on the higher-order dissipative solitons is investigated. The obtained results are novel solutions for non-integrable/damped Kawahara equation. The EDT4RK method is a powerful and a fourth-order accurate technique for obtaining numerical solutions with high accuracy and longtime stable.