Abstract
The dynamic structures of ion acoustic waves in an unmagnetized plasma with q-nonextensive electrons and positrons are investigated applying the bifurcation theory of planar dynamical systems through direct approach. Model equations are transformed to a planar dynamical system using a traveling wave transformation. Using the bifurcations of planar dynamical system, the existence of solitary and periodic waves is shown. We have obtained new analytical forms for solitary and periodic waves depending on parameters $$p, q, \sigma $$ and v. Considering an external periodic perturbation, the chaotic behavior of nonlinear ion acoustic waves is presented. Depending upon different regimes of the nonextensive parameter q, the effect of q is shown on chaotic motions of ion acoustic waves with fixed values of other parameters $$p,\sigma $$ and v. It is seen that the unperturbed system has the solitary and periodic wave solutions, but the perturbed dynamical system has chaotic motions for same values of parameters $$p, q, \sigma $$ and v.
Highlights
The nineteenth century and half of twentieth century can be viewed as the triumph of linear physics, which started with Maxwell’s equations, based on a linear formalism emphasizing a superposition principle
To generalize the usual Boltzmann–Gibbs thermostatics according to the demand of thermodynamical or statistical description of nonextensive systems, the standard Boltzmann–Gibbs appProach based on the extensive entropy measure S 1⁄4 Àk i pilnpi, where k is the Boltzmann constant and pi denotes the probabilities of microscopic configurations modified by Tsallis [41, 4P2] in the following nonextensive form of entropy
We have addressed the dynamic structures of ion acoustic waves in an unmagnetized plasma with q-nonextensive electrons and positrons using the bifurcation theory of planar dynamical systems through direct approach
Summary
The nineteenth century and half of twentieth century can be viewed as the triumph of linear physics, which started with Maxwell’s equations, based on a linear formalism emphasizing a superposition principle. Shahmansouri and Alinejad [53] studied the effect of electron nonextensivity on oblique propagation of arbitrary ion acoustic waves in a magnetized plasma. Shahmansouri and Astaraki [54] investigated the transverse perturbation on three-dimensional ion acoustic waves in electron–positron–ion plasma with highenergy tail electron and positron distribution. Samanta et al [57] studied bifurcations of dust-ion acoustic traveling waves in a magnetized dusty plasma with a q-nonextensive electron velocity distribution. We present the chaotic behavior of the perturbed system in ‘‘Chaos in the perturbed system’’ and ‘‘Conclusions’’ sections are kept for conclusions
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