Volume 75, Issue 8

Nonlinear properties of ion-acoustic waves (IAWs) are studied in electron-ion (EI) degenerate plasma with the electron exchange-correlation effects by using the quantum hydrodynamic (QHD) model. To investigate arbitrary amplitude IAWs, we have reduced the model equations into a system of ordinary differential equations using a traveling wave transformation. Computational investigations have been performed to examine the combined effect of Bohm potential and exchange-correlation potential significantly modifies the dynamics of IAWs by employing the concept of dynamical systems. The equilibrium points of the model are determined and its stability natures are analyzed. The phase portrait and Poincaré return map of the dynamical system are displayed numerically. Quasiperiodic as well as chaotic dynamics of the system are confirmed through the Poincaré return map diagrams.

Dynamical properties of nonlinear ion-acoustic waves (IAWs) in multi-pair plasmas (MPPs) constituting adiabatic ion fluids of positive and negative charges, and q -nonextensive electrons and positrons are examined. The nonlinear Schrödinger equation (NLSE) is considered to study the dynamics of IAWs in a nonextensive MPP system. Bifurcation of the dynamical system obtained from the NLSE shows that the system supports various wave forms such as, nonlinear periodic wave, kink and anti-kink waves in different ranges of q . The analytical solutions for ion-acoustic nonlinear periodic wave, kink and anti-kink waves are obtained. The impacts of system parameters such as, nonextensive parameter ( q ), mass ratio of negative and positive ions ( μ 1 ), number density ratio of positive and negative ions ( μ 2 ), number density ratio of positrons and negative ions ( μ p ), temperature ratio of positive ions and electrons ( σ 2 ) and temperature ratio of electrons and positrons (δ) on IAW solutions are bestowed. The results of this study are applicable to understand different dynamical behaviors of nonlinear IAWs found in the Earth’s ionosphere, such as, D-region [H + , O2−${\mathrm{O}}_{2}^{-}$] and F-region [H + , H − ] and multipair plasma system laboratory [C + , C − ].

In this paper, we consider the well-known Vallis model for El Niño driven by an external excitation. The bifurcation studies on the driven Vallis model are conducted with different control parameters. Then we discuss about the taming of the Hopf bifurcation by varying the driving function. We could note that the system changes its state from stable steady state to oscillatory state and vice versa which is achieved by changing the driving function. Finally, two parameter bifurcation plots are derived to show that impact of the driving function on the system bifurcation points.

Exact force-free plasma equilibria satisfying the nonlinear Beltrami equation are derived. The construction is based on a nonlinear transformation that allows to get from any solution to the linear Beltrami equation a one-parametric family of exact solutions to the nonlinear one. Exact force-free plasma equilibria connected with the Sine-Gordon equation are presented.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t -periodic for large t if the Dirichlet boundary datum is periodic in t . Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t , then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

In the article, the effects of the thermal viscosity and magnetohydrodynamic on the peristalsis of nanofluid are analyzed. The dominant neutralization is deduced through long wavelength approximation. The analytical solution of velocity and temperature is extracted by using steady perturbation. The pressure gradient and friction forces are obtained. Numerical results are calculated and contrasted with the debated theoretical results. These results are calculated for various values of Hartmann number, variable viscosity parameter and amplitude ratio. It is observed that the pressure gradient is reduced with an increase in the thermal viscosity parameter and that the Hartmann number enhances the pressure difference.