Nonlinear evolution of Alfvénic wave packets

Alfvén waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrödinger evolution equation (DNLS) to solutions of the compressible MHD equations. We find that the soliton solutions of the DNLS equation are not stable solutions of Hall‐MHD—they evolve and dissipate with time. Although such solitons may serve as approximate initial conditions to the Hall‐MHD equations, they are not stationary solutions. This may account for the absence of soliton‐like wave forms in the free‐flowing solar wind.