Formation of quasiparallel Alfvén solitons

Abstract

The formation of quasiparallel Alfvén solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schrödinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schrödinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasiparallel Alfvén waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfvén solitons.