The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated. The existence of the travelling wave solutions is discussed. The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented. Both suggest that the Korteweg-de Vries (KdV) system is modulationally stable. Besides, the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented. It is shown that these interacting waves alternately exchange their energy during propagation. The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves. It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma. However, few researchers have considered such magnetohydrodynamic (MHD) wave interactions in plasma. It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.
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