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Nonlinear periodic coupled Alfvén and ion-acoustic wave structures in plasmas

The nonlinear propagation of coupled Alfvén and ion-acoustic waves is investigated in homogeneous, magnetized and collisionless electron-ion plasma. The ion parallel motion is included in the model so that ion-acoustic wave couples with Alfvén wave in plasmas. In linear limit, the dispersion relation of coupled Alfvén and ion-acoustic waves is derived and its dispersion effects are investigated analytically as well as numerically using laboratory plasma parameters, given in the literature. Using reductive perturbation method, the Korteweg–de Vries (KdV) equation is derived for nonlinear coupled Alfvén and ion-acoustic waves in plasmas by applying appropriate periodic boundary conditions. The cnoidal wave solution of coupled Alfvén and ion-acoustic waves in terms of Jacobian elliptic function (cn) is obtained and its soliton solution is also investigated. The numerical plots of cnoidal wave and soliton structures with variations of plasma β (defined as the ratio of kinetic pressure to magnetic pressure) and obliqueness of the wave propagation with respect to external magnetic field are presented for illustration. It is found that low amplitude compressive structures of nonlinear coupled Alfvén and ion-acoustic waves exist in a magnetized plasma, which moves with sub-Alfvénic wave speed.