Effect of polarization force on small amplitude dust kinetic Alfvén solitary and rogue waves in a nonextensive plasma

In the present investigation, the effect of polarization force on small amplitude dust kinetic Alfvén solitary waves (DKASWs) and dust kinetic Alfvén rogue waves (DKARWs) has been studied in a dusty plasma, comprising of negatively charged dust fluid, and q-nonextensive distributed electrons and positive ions. From the solution of Korteweg-de Vries (KdV) equation, small amplitude DKASWs have been studied. The non-linear Schrödinger equation (NLSE) has been derived from the KdV equation to study the DKARWs from its rational solution. Numerical analysis of solution of KdV equation reveals the existence of positive potential DKASWs. The combined effects of polarization force, nonextensivity of ions, plasma beta, angle of propagation of the wave with respect to the magnetic field and the ratio of number density of electrons to the number density of ions have been analyzed on the characteristics of DKASWs and DKARWs.