Dynamics of low dimensional model for weakly relativistic Zakharov equations for plasmas

In the present paper, the nonlinear interaction between Langmuir waves and ion acoustic waves described by the one-dimensional Zakharov equations (ZEs) for relativistic plasmas are investigated formulating a low dimensional model. Equilibrium points of the model are found and it is shown that the existence and stability conditions of the equilibrium point depend on the relativistic parameter. Computational investigations are carried out to examine the effects of relativistic parameter and other plasma parameters on the dynamics of the model. Power spectrum analysis using fast fourier transform and also construction of first return map confirm that periodic, quasi-periodic, and chaotic type solution exist for both relativistic as well as in non-relativistic case. Existence of supercritical Hopf bifurcation is noted in the system for two critical plasmon numbers