Recent progress on the inverse scattering theory for ideal Alfvén waves

The Alfvén waves are fundamental wave phenomena in magnetized plasmas. Mathematically, the dynamics of Alfvén waves are governed by a system of nonlinear partial differential equations called the magnetohydrodynamics (MHD) equations. Let us introduce some recent results about inverse scattering of Alfvén waves in ideal MHD, which are intended to establish the relationship between Alfvén waves emanating from the plasma and their scattering fields at infinities.The proof is mainly based on the weighted energy estimates. Moreover, the null structure inherent in MHD equations is thoroughly examined, especially when we estimate the pressure term.