Small amplitude propagation and quasielastic head-on collision of ion-acoustic solitary waves (IASWs) are investigated in a degenerate Thomas–Fermi electron-positron-ion magnetized plasma using extended Poincare–Lighthill–Kuo reductive perturbation method for both ultrarelativistic and nonrelativistic electron/positron degeneracy cases. It is observed that both bright- and dark-type solitary shapes can exist in such plasma, depending on two critical values. The shape of ion-acoustic solitary structures as well as sign of their collision phase shifts are both determined by the same critical values. It is further revealed that relativistic degeneracy of electrons/positrons has significant effect on the propagation as well as interaction of IASWs.

Propagation and head-on collisions of ion-acoustic solitons in a Thomas–Fermi magnetoplasma: Relativistic degeneracy effects

Head-on collision of ion-acoustic solitary waves in a weakly relativistic electron–positron–ion plasma

The head-on collision between two ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma has been investigated. By using the extended Poincare-Lighthill-Kuo perturbation method, we obtain the KdV equation and the analytical phase shift after the head-on collision of two solitary waves in this three-component plasma. The effects of the ratio of electron temperature to positron temperature, and the ratio of the number density of positrons to that of electrons on the phase shift are studied. It is found that these parameters can significantly influence the phase shifts of the solitons. Moreover, the compressive solitary wave can propagate in this system.

Head-on collision of ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma

Small-amplitude ion-acoustic double layers (IA-DLs) in a plasma with superthermal electrons and thermal positrons are investigated. Due to the electron superthermality and the relative fraction of positrons, our plasma model can admit compressive as well as rarefactive IA-DLs. As the electrons evolve toward their thermodynamic equilibrium, the negative IA-DL shrinks and, beyond a certain critical value of the electron spectral index κc, develops into a positive structure allowing therefore the existence of compressive IA-DLs. This critical value is lowered as the number of positrons becomes important. As the superthermal character of the plasma increases, the threshold pc above which only compressive IA-DLs are admitted is shifted toward higher values. Our investigation may help to understand the DL structures observed in the ionosphere and the auroral acceleration regions.

Small amplitude ion-acoustic double layers in a plasma with superthermal electrons and thermal positrons

The problem of arbitrary amplitude ion acoustic solitary waves in a plasma with Boltzmann distributed positrons and superthermal electrons is addressed. The domain of their allowable Mach numbers is shifted towards lower values as the positron-to-electron density ratio p is increased. Beyond a certain critical value of p only subsonic ion-acoustic solitons are admitted. This threshold for the onset of subsonic ion-acoustic solitons is lowered as the superthermal character of the plasma is increased. In the limit of small spectral index κ, the ion-acoustic solitons are subsonic over the entire range of p. Cusped ion-acoustic solitons may arise as the electrons evolve far away from their thermodynamic equilibrium. Our results should help to understand the localized structures that may occur in space plasmas.

http://iopscience.iop.org/article/10.1088/0031-8949/79/06/065503/pdf

Ion acoustic solitary waves in a plasma with superthermal electrons and positrons

Effects of positron density and temperature on ion acoustic dressed solitons in an electron–positron–ion plasma

This paper presents a defect correction scheme based on finite-difference discretization for a singularly perturbed convection-dominated diffusion problem. The solution of this class of problems exhibits a multiscale character. There are narrow regions in which the solution grows exponentially and reveals layer behaviour. The defect correction method that we propose improves the efficiency of a numerical solution through iterative improvement and generates a stable higher-order method over an adaptive non-uniform polynomial-Shishkin mesh. An extensive theoretical analysis is presented, which establishes that the method is second-order uniformly convergent and highly stable. The convergence obtained is optimal because it is free from any logarithmic term. The numerical result for two model problems is presented, agreeing with the theoretical estimates. Furthermore, we compare the results with those of other non-uniform mesh found in the literature. 

A higher-order uniformly convergent defect correction method for singularly perturbed convection-diffusion problems on an adaptive mesh

A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary condition

We propose a hybrid numerical scheme to discretize a class of singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions on an equidistributed grid. The hybrid difference scheme is developed by using a modified backward difference scheme in time, a combination of the cubic spline and exponential spline difference scheme in space. The proposed scheme uses a cubic spline difference scheme for the discretization of robin‐boundary conditions. For the time discretization of the problem, we use the standard uniform mesh while a layer adapted equidistributed grid is generated for the spatial discretization. By equidistributing a curvature‐based monitor function, the spatial adaptive grid is able to capture the presence of parabolic boundary layers without using any prior information about the solution. Parameter uniform error estimates are derived to illustrate an optimal convergence of first‐order in time and second‐order in space for the proposed discretization. The accuracy of the proposed scheme is confirmed by the numerical experiments that underpin the theoretical analysis.

A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions

Aditya Kaushik

Papers

Effects of positron density and temperature on ion acoustic dressed solitons in an electron–positron–ion plasma

A higher-order uniformly convergent defect correction method for singularly perturbed convection-diffusion problems on an adaptive mesh

A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary condition

A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions

A uniformly convergent defect correction method for parabolic singular perturbation problems with a large delay