Nonlinear interaction between three kinetic Alfvén waves

Using Hall-MHD theory, we focus on the resonant interaction between three kinetic Alfven waves. We thus derive three coupled equations which govern this process. It turns out that these equations contain the same coupling coefficient, directly showing that they satisfy the Manley–Rowe relations. The coupling coefficient can be written in a comparatively very simple form, that has not been deduced before. The decay rate, when a pump kinetic Alfven wave decays into two similar Alfven waves, is therefore easily estimated for plasmas of astrophysical interest.