Small-amplitude supernonlinear ion-acoustic waves (SIAWs) are examined in a multicomponent electron-ion plasma that is composed of fluid cold ions and two temperature q-nonextensive hot and cold electrons. Implementing the reductive perturbation method, four nonlinear evolution equations are derived: the Korteweg-de-Vries (KdV) equation, the modified KdV (mKdV) equation, the further modified KdV equation, and the modified Gardner (mG) equation. Employing the traveling wave transformation, the nonlinear evolution equations are deduced to their corresponding planar dynamical systems. Applying phase plane theory of dynamical systems, phase portrait profiles including nonlinear homoclinic trajectories, nonlinear periodic trajectories from the KdV equation, and additional supernonlinear periodic trajectories are presented for ion-acoustic waves (IAWs) from the modified KdV equation. Furthermore, supersolitons corresponding to the supernonlinear homoclinic trajectory of IAWs under the modified Gardner equation are shown in a phase plane and confirmed by the potential plot with a specified set of physical parameters q, σc, σh, f, and U. Nonlinear and SIAWs are displayed using computation for distinct parametric values.
Qualitative analysis of the positron acoustic (PA) waves in a four-component plasma system consisting of static positive ions, mobile cold positron, and Kaniadakis distributed hot positrons and electrons is investigated. Using the reductive perturbation technique, the Korteweg-de Vries (K-dV) equation and the modified KdV equation are derived for the PA waves. Variations of the total energy of the conservative systems corresponding to the KdV and mKdV equations are presented. Applying numerical computations, effect of parameter (κ), number density ratio (μ1) of electrons to ions and number density (μ2) of hot positrons to ions, and speed (U) of the traveling wave are discussed on the positron acoustic solitary wave solutions of the KdV and mKdV equations. Furthermore, it is found that the parameter κ has no effect on the solitary wave solution of the KdV equation, whereas it has significant effect on the solitary wave solution of the modified KdV equation. Considering an external periodic perturbation, the perturbed dynamical systems corresponding to the KdV and mKdV equations are analyzed by employing three dimensional phase portrait analysis, time series analysis, and Poincare section. Chaotic motions of the perturbed PA waves occur through the quasiperiodic route to chaos.
Phase plane analysis of small amplitude electron-acoustic supernonlinear and nonlinear waves in a magnetized nonextensive electron-ion plasma is examined. These electron-acoustic waves (EAWs) are studied based on the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations. The dynamical systems for both the KdV and mKdV equations are formed using the propagating wave transfiguration. Phase plane analyses of EAWs corresponding to the KdV and mKdV equations are shown. Analytical solution corresponding to the electron-acoustic solitary wave for the KdV equation is derived. Analytical forms of kink, anti-kink and periodic wave solutions in ranges −1 < q < 0 and 0 < q < 1 are obtained for the mKdV equation. Superperiodic EAWs under the mKdV equation in the range q > 1 are shown numerically. Existence of small amplitude superperiodic EAWs under the mKdV equation is shown for the first time in a magnetized nonextensive electron-ion plasma using the concept of planar dynamical systems. Effects of system parameters on different traveling wave solutions of EAWs are displayed. Outcome of the study can be implemented to understand nonlinear and supernonlinear EAWs in space and atmosphere, such as, auroral zones and magnetosphere.
The nonlinear ion-acoustic waves (IAWs) in a space plasma are capable of exhibiting chaotic dynamics which can be applied to cryptography. Dynamical properties of IAWs are examined using the direct method in plasmas composed of positive and negative ions and nonextensive distributed electrons. Applying the wave transformation, the governing equations are deduced into a dynamical system (DS). Supernonlinear and nonlinear periodic IAWs are presented through phase plane analysis. The analytical periodic wave solution for IAW is obtained. Under the influence of an external periodic force, the DS is transformed to a perturbed system. The perturbed DS describes multistability property of IAWs with change of initial conditions. The multistability behavior features coexisting trajectories such as, quasiperiodic, multiperiodic and chaotic trajectories of the perturbed DS. The chaotic feature in the perturbed DS is supported by Lyapunov exponents. This interesting behavior in the windows of chaotic dynamics is exploited to design efficient encryption algorithm. First SHA-512 is used to compute the hash digest of the plain image which is then used to update the initial seed of the chaotic IAWs system. Note that SHA-512 uses one-way function to map input data to the output, consequently it is quite impossible to break the proposed encryption technique. Second DNA coding is used to confuse and diffuse the DNA version of the plain image. The diffused image follows DNA decoding process leading to the cipher image. The security performance is evaluated using some well-known metrics and results indicate that the proposed cryptosystem can resist most of existing cryptanalysis techniques. In addition complexity analysis shows the possibility of practical implementation of the proposed algorithm.
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