In this paper, resonant interactions among three shear-Alfvén waves is investigated in weak incompressible magnetohydrodynamics (MHD) turbulence, neglecting interactions involving the pseudo-Alfvén waves. It is found that these interactions lead to a wave kinetic equation that has the same compact form as the full nonlinear MHD system in the highly anisotropic limit (k⊥⪢k‖). These results have important implications for interpreting the effects of resonant three-wave interactions among shear-Alfvén waves throughout k space. In particular, it shows that resonant three-wave interactions involving only shear-Alfvén waves attempt to set up a k⊥nsf(k‖) 3D shear-Alfvén-wave spectrum (with −4<ns<−2, and f an arbitrary function depending on the initial conditions). The results also provide a framework for estimating the time scale on which the three shear-Alfvén-wave interactions transfer energy to larger k⊥ everywhere in the k⊥-k‖ plane. The compatibility of the results with previous predictions and the possible astrophysical implications of these extended spectral solutions for anisotropic plasmas is discussed.
