Studying the dissipation effects on the formation of the nonlinear plasmons

Excitation of plasmons at the surface of the overdense plasma is responsible for the transition of the energy of electromagnetic waves in the plasma. The effects of the nonlinearities and dispersions are inevitable in the overdense plasma. In this article, it is investigated these effects on the excitation of the surface waves on the interface between the plasma and vacuum. Using the perturbation expansion, the equations are analytically solved up to the second order. By studying the dispersion relation, the conditions are obtained for the formation of the surface waves in both linear and second-order approximations. The results show that the dissipation effects have important outcomes on the dispersion relation and its consequences. Specifically, in the presence of these effects, the frequency regime suitable for the surface wave excitations becomes wider.  At the second-order approximation, the dissipation effects lead to the excitation of the surface waves at lower frequencies.