Propagation of solitons of the Derivative Nonlinear Schrodinger equation in a plasma with fluctuating density

The propagation of quasi-parallel nonlinear small-amplitude magnetohydrodynamic waves in a cold Hall plasma with fluctuating density is studied. The density is assumed to be a homogeneous random function of one spatial variable. The modified Derivative Nonlinear Schrodinger equation (DNLS) is derived with the use of the mean waveform method developed by Gurevich, Jeffrey, and Pelinovsky [Wave Motion 17, 287 (1993)], which is the generalization of the reductive perturbation method for nonlinear waves propagating in random media. This equation differs from the standard DNLS equation by one additional term describing the interaction of nonlinear waves with random density fluctuations. As an example of the use of the modified DNLS equation, the quasi-adiabatic evolution of a one-parametric DNLS soliton propagating through a plasma with fluctuating density is studied.