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 obliquely nonlinear acoustic solitary propagation in a relativistically quantum magnetized electron-positron (e-p) plasma in the presence of the external magnetic field as well as the stationary ions for neutralizing the plasma background was studied. By considering the dynamic of the fluid e-p quantum and by using the quantum hydrodynamics model and the standard reductive perturbation technique, the Zakharov-Kuznetsov (ZK) equation is derived for small but finite amplitude waves and the solitary wave solution for the parameters relevant to dense astrophysical objects such as white dwarf stars is obtained. The numerical results show that the relativistic effects lead to propagate the electrostatic bell shape structures in quantum e-p plasmas like those in classical pair-ion or pair species for relativistic plasmas. It is also observed that by increasing the relativistic effects, the amplitude and width of the e-p acoustic solitary wave will decrease. In addition, the wave amplitude increases as positron density decreases in magnetized e-p plasmas. It is indicated that by increasing the strength of the magnetic field, the width of the soliton reduces and it becomes sharper. At the end, we have analytically and numerically shown that the pulse soliton solution of the ZK equation is unstable and have traced the dependence of the instability growth rate on electron density. It is found that by considering the relativistic pressure, the instability of the soliton pulse can be reduced. The results can be useful to study the obliquely nonlinear propagation of small amplitude localized structures in magnetized quantum e-p plasmas and be applicable to understand the particle and energy transport mechanism in compact stars such as white dwarfs, where the effects of relativistic electron degeneracy become important.
In this research, the modulation of a weakly three-dimensional electrostatic ion-acoustic wave (IAW) is studied in dense magnetoplasma consisting of relativistic degenerate inertialess electrons and nondegenerate inertial thermal ions. It is assumed that the degeneracy pressure law for electrons follows the Chandrasekhar equation of state. The standard reductive perturbation theory has been applied to obtain the corresponding three-dimensional nonlinear Schrodinger equation, where the nonlinearity is in balance with the dispersive terms. This equation governs the dynamics and shows the slow modulation of the IAWs. This equation also been influenced not only by the external magnetic field but also by the usual plasma parameters. The numerical results indicate that new instability regimes arise when we consider the relativistic parameter ( μe), the ion to electron temperature ratio (σi), and the normalized ion cyclotron frequency (ωci) which though cannot be observed in the unmagnetized case can considerably modify the profiles of the envelope magneto acoustic solitons. Also, some significant explicit critical frequencies are obtained, which permit us to consider new regimes different from the usual unmagnetized plasma for propagation of IAWs in the magnetoplasma, which may exist in space or astrophysics.
Bifurcation analysis of ion-acoustic waves in complex plasmas in the presence of adiabatic trapped electrons and warm ions is studied. Using bifurcation theory of dynamical structure, the Hamiltonian system inculpated electrostatic potential is derived. Effects of physical parameters, such as T and σ i , are shown on the analytical solitary wave solution. The numerical results show that parameters T and σ i affect significantly on nonlinear electrostatic solitary waves. By adding an external periodic perturbation to unperturbed Hamiltonian system, we investigate quasiperiodic structure of the perturbed Hamiltonian system.
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