Nonlinear Dispersive Rayleigh–Taylor Instabilities in Magnetohydrodynamic Flows

Abstract

In this paper a weakly nonlinear theory of wave propagation in superposed fluids in the presence of magnetic fields is presented. The equations governing the evolution of the amplitude of the progressive as well as the standing waves are reported. The nonlinear evolution of Rayleigh–Taylor instability (RTI) is examined in 2+1 dimensions in the context of Magnetohydrodynamics (MHD). This can be incorporated in studying the envelope properties of the 2+1 dimensional wave packet. We converted the resulting nonlinear equation (nonlinear Schrödinger (NLS) equation) for the evolution of the wave packets in 2+1 dimensions using the function transformation method into a sinh-Gordon equation and other nonlinear evolution equations. The latter depend only on one function ζ and we obtained several classes of general soliton solutions of these equations, leading to classes of soliton solutions of the 2+1 dimensional NLS equation. It contains some interesting specific solutions such as the N multiple solitons, the propagational breathers and the quadratic solitons, which contains the circular, elliptic and hyperbolic shape solitons. A stability analysis of these solutions is performed.