The Two Component Derivative Nonlinear Schrodinger Equation

Abstract

With the results presented in this paper it is therefore possible t o investigate the modulational stability of circularly polarised waves of arbitrary polarisation in the manner of Mj$lhus [ 71 forIn this paper we present the solution to the two component non-linear derivative Schr6dinger equation enables modulational stability of circularly polarised long Alfven waves of arbitrary polarisation to be investigated. The covariant formalism used is easily adapted to solve the n-component non-linear derivative Schrodinger equation.the single component derivative nonlinear Schrodinger equation although we d o not pursue this here.

The brightN-soliton solution of a multi-component modified nonlinear Schrödinger equation

“…In the context of plasma physics, the twocomponent system with µ = 0 is a model equation for the propagation of polarized Alfvén waves. The single bright soliton solution to this system has been obtained by means of the IST [8]. The two-component system with µ = 0 and γ = 0 has been derived as a model for describing the propagation of ultra-short pulses in birefringent optical fibers, together with its soliton solutions [9].…”

Hybrid Ermakov-Painlevé IV Systems

“…The procedure is motivated by the occurrence of such a ErmakovPainlevé IV system as a symmetry reduction of an N-component derivative nonlinear Schrödinger system. In terms of physical applications, two-component derivative NLS systems were originally derived by Morris and Dodd [32] in a study of the modulational stability of circularly polarized long Alfvén waves. Alfvén solitonic phenomena in such coupled derivative NLS systems in plasma physics have subsequently been investigated by Xu et al in [63] while Darboux transformations for two-component derivative NLS systems have been constructed by Ling and Liu [31].…”

On the Dissipative Evolution Equations Associated with the Zakharov-Shabat System with a Quadratic Spectral Parameter

“…Gerzhikov et al also considered this case [6]. Morris and Dodd considered the two-component derivative nonlinear Schrödinger equation using a larger scattering problem (i.e., n = 3) [15]. Sasaki derived a Hamiltonian structure for the evolution (4.2) [16].…”