On the propagation of cnoidal wave and overtaking collision of slow shear Alfvén solitons in low β magnetized plasmas

Abstract

The overtaking collisional phenomenon of slow shear Alfvén solitons are studied in a low beta (β = kinetic pressure/magnetic pressure) collisionless, magnetized plasma consisting of electron and ion fluids. By employing a reductive perturbation technique, the Korteweg–de Vries (KdV) equation is deduced for investigating the nonlinear slow shear Alfvén wave. Before embarking on the study of the overtaking collisions, the stability analysis of the KdV equation is studied using the bifurcation theory. Also, a nonlinear periodic solution of the KdV equation is derived for the first time in the Weierstrass elliptic function formula. Moreover, the condition for converting the Weierstrass elliptic function expression to soliton is discussed. Furthermore, it is found that only density dip (rarefactive) solitons are formed in the super-Alfvénic regime. The next step includes the use of the Hirota bilinear method, which results in two and three shear Alfvén soliton solutions and their subsequent phase shifts. The influence of the plasma parameters on the amplitude as well as width of the slow shear Alfvén wave solitons are examined analytically and numerically. We also find out the profiles of overtaking interaction of slow shear Alfvén dip solitons having different amplitudes and speeds numerically. This study is important for understanding the phenomena of nonlinear slow shear Alfvén wave structures both in space and in laboratory plasmas.