K-P Burgers Equation for the Decayof Solitary Magnetosonic Waves Propagating Obliquelyin a Warm Collisional Plasma

Abstract

A nonlinear evolution equation governing the two dimensional propagation of fast and slow magnetosonic modes in a warm collisional plasma has been derived. This equation is a combination of Kadomtsev-Petviashvili (K-P) equation and the Burgers equation. The two dimensional K-P equation has two types of solitary wave solutions depending on the sign of the coefficients. One type is the usual planar type, the other is the lump solution. Both types of solitary wave solutions decay with time in the weak collisional limit. The two dimensional features of the amplitude and width of the lump or algebraic soliton have been discussed and the decay rates computed numerically. The decay rates depend on plasma beta and on the angle of propagation and the rates are different for the fast and the slow waves. At a certain angle of propagation the decay rates of both the modes are equal in the case of low beta plasma. Because of 2-D effects, the slow mode, although it has a lower collisional decay rate than the fast mode,...