Spiky Soliton in Circular Polarized Alfvén Wave

Abstract

A new type of nonlinear evolution equation for the Alfvén waves, propagating parallel to the magnetic field, is now registered to the completely integrable family of nonlinear evolution equations. In spite of the extensive studies of Kaup and Newell, and of Kawata and Inoue, these analysis have been dealing with solutions for restricted boundary conditions. The present paper presents full account of stationary solitary wave solutions for the plane wave boundary condition. The obtained results exhibit peculiar structure of spiky modulation of amplitude and phase, which arises from the derivative nonlinear coupling term. A nonlinear equation for complex amplitude associated with the carrier wave is shown to be a mixed type of nonlinear Schrödinger equation, having an ordinary cubic nonlinear Schrödinger equation, having an ordinary cubic nonlinear term and the derivative of cubic nonlinear term.