A new equation in two dimensional fast magnetoacoustic shock waves in electron-positron-ion plasmas.

Nonlinear properties of the two dimensional fast magnetoacoustic waves are studied in a three-component plasma comprising of electrons, positrons, and ions. In this regard, Kadomtsev–Petviashvili–Burger (KPB) equation is derived using the small amplitude perturbation expansion method. Under the condition that the electron and positron inertia are ignored, Burger–Kadomtsev–Petviashvili (Burger-KP) for a fast magnetoacoustic wave is derived for the first time, to the best of author’s knowledge. The solutions of both KPB and Burger-KP equations are obtained using the tangent hyperbolic method. The effects of positron concentration, kinematic viscosity, and plasma β are explored both for the KPB and the Burger-KP shock waves and the differences between the two are highlighted. The present investigation may have relevance in the study of nonlinear electromagnetic shock waves both in laboratory and astrophysical plasmas. [ABSTRACT FROM AUTHOR]