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

Abstract

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 Schrödinger equation ͑DNLS͒ is derived with the use of the mean waveform method developed by Gurevich, Jeffrey, and Pelinovsky ͓Wave Motion 17, 287 ͑1993͔͒, 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.

N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

“…Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons. The derivative nonlinear Schrödinger (DNLS) equation is an integrable model describing various nonlinear waves such as nonlinear Alfvén waves in space plasma(see, e.g., [1,2,3,4,5,6,7]), sub-picosecond pulses in single mode optical fibers(see, e.g., [8,9,10,11,12]), and weak nonlinear electromagnetic waves in ferromagnetic [13], antiferromagnetic [14], and dielectric[15] systems under external magnetic fields. Both of vanishing boundary conditions (VBC) and nonvanishing boundary conditions (NVBC) for the DNLS equation are physically significant.…”

Quasi-Particle Theory of Alfven Soliton Interaction in Plasmas

“…Also, the following notations are used (Mamun, 1999;Mio et al, 1976;Mjolhus and Wyller, 1988;Ozawa, 1996;Ruderman, 2002;Sen and Chowdhury, 1987;Wyller and Mjolhus, 1984)…”

Solitonic interactions, Darboux transformation and double Wronskian solutions for a variable-coefficient derivative nonlinear Schrödinger equation in the inhomogeneous plasmas

“…One of them, the derivative nonlinear Schrödinger equation, can be used to describe such physical phenomena as the Alfvén waves in space plasma [18][19][20][21][22][23], femtosecond pulses in the single-mode optical fibers [24][25][26][27], weak nonlinear electromagnetic waves in (anti-)ferromagnetic or dielectric systems under the external magnetic fields [28][29][30]. With the inhomogeneity of the real plasma environment (i.e., the fluctuations of the density, temperature and magnetic fields) considered [31][32][33], attention has been paid to the variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equations [34][35][36][37][38][39].…”