Nonlinear dispersive Alfvén waves interaction in magnetized plasma

Abstract

This study is concerned with the nonlinear interactions between pairs of intersecting Alfvén waves in a magnetized plasma and used the modified Korteweg–de Vries equation to study nonlinear interactions. The modulation instability analysis shows the existence of periodic traveling wave solution in the system. Two different types of waves interaction solutions, namely, the periodic wave interaction solutions and the solitary wave interaction ones, are captured analytically. It is found that the wave resonance for the periodic waves interaction could happen as various wave numbers are nearly the same. In this case, the subsidiary waves could not be neglected. It is also found that the interaction for solitary waves, different solitons eventually regain their original states. The solitons with higher energy possess more speed as compared to the low energy solitons. The phenomenon of Alfvén wave interaction can be of importance for understanding the transport mechanism of magnetic waves in various processes of heating and transport of energy in space, solar wind, and astrophysical plasma.