Formula omitted]-soliton asymptotic analysis on the Gerdjikov–Ivanov equation for the Alfvén waves in a plasma

Abstract

Gerdjikov–Ivanov equation describes the propagation of the weakly nonlinear and dispersive Alfvén waves along the ambient electromagnetic field in a partially ionized plasma in the presence of the Hall, ambipolar, and Ohmic effects. With respect to the transverse components of the electromagnetic field to the lowest order, N solitons in the determinant form are derived and analyzed via the asymptotic analysis on the basis of an existing binary DT and an existing Lax pair, where N is a positive integer. Without loss of generality, expressions of the N asymptotic solitons in the determinant form are obtained, from which we can obtain the amplitudes, positions, velocities and phase shifts of the N asymptotic solitons. Those results reveal that the interaction among the N solitons is elastic. When N=3, we graphically illustrate the elastic interaction among the three solitons. This work may provide a physical mechanism for the generations and interactions of the Alfvén solitons in the magnetized plasmas.