Fast magnetohydrodynamic cnoidal waves and solitons in electron-positron plasma

Abstract

Linear and nonlinear propagation of fast magnetohydrodynamic waves (or magnetoacoustic waves) are studied in homogeneous, magnetized and warm collisionless electron-positron (e-p) plasma by using two fluid magnetohydrodynamic model. In the linear limit, the wave dispersion relation is obtained and wave dispersion effect which appears through inertial length in e-p plasma system is also discussed. Using reductive perturbation method, the Korteweg-de Vries (KdV) equation for small but finite wave amplitude of magnetoacoustic waves is derived with appropriate boundary conditions. The cnoidal wave and soliton solutions are obtained using well known Sagdeev potential approach for magnetoacoustic waves in e-p plasmas propagating in the direction perpendicular to the external magnetic field. The phase portrait analysis and numerical illustration of magnetoacoustic cnoidal waves and solitons is also presented by using the parameters such as magnetic field intensity, plasma density and temperature of electron and positron fluids for astrophysical plasma situations exist in the literature.

Nonlinear periodic coupled Alfvén and ion-acoustic wave structures in plasmas

“…, have been used to obtain equation (38), so that c 0 is now independent of ξ and τ, and this constant gives just a shift in the speed of the nonlinear structures. Now in order to find the steady state solution of KdV equation (i.e., equation ( 38)), we follow the same method as depicted in [51,52]. For this purpose, we set another variable η such that h x t = -V (where V is the speed of the nonlinear wave structure in comoving frame).…”