Abstract
Two novel analytical solutions to the damped Gardner Kawahara equation and its related equations are reported. Using a suitable ansatz and with the help of the exact solutions of the undamped Gardner Kawahara equation, two general high-accurate approximate analytical solutions are derived. Moreover, the Crank–Nicolson implicit finite difference method is introduced for analyzing the evolution equation numerically. The comparison between the obtained solutions is examined. All the obtained solutions are able to investigate many types of the dissipative traveling wave solutions such as the dissipative solitary and cnoidal waves. Also, the obtained solutions help many researchers understand the mechanisms underlying a variety of nonlinear phenomena that can propagate in optical fiber, physics of plasmas, fluid mechanics, water tank, oceans, and seas. The obtained solutions could be applied for investigating the characteristics of the dissipative higher-order solitary and cnoidal waves in electronegative plasmas. Numerical results depending on the physical plasma parameters are presented.
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