Qualitative Behavior of Ion Acoustic Waves in Nonextensive Unmagnetized Plasmas

The qualitative behaviors of ion acoustic waves in unmagnetized plasma with q-nonextensive cool and hot electrons are investigated using the bifurcation theory of planar dynamical systems. Using a traveling wave transformation and initial conditions, basic equations are transformed to a planar dynamical system. Using numerical computations, all possible phase portraits of the dynamical system are presented. Corresponding to homoclinic and periodic orbits of the phase portraits, three analytical forms of solitary and periodic wave solutions are derived depending on nonextensive parameter (q), ratio of unperturbed densities of cold electrons and ions (p), temperature ratio of cold and hot electrons (sigma) and speed (nu); of the traveling wave. Considering an external periodic perturbation, the quasiperiodic and chaotic behaviours of ion acoustic waves are presented. Depending upon different ranges of nonextensive parameter q, the effect of q is shown on quasiperiodic and chaotic behaviours of ion acoustic waves with fixed value of p, sigma and nu.