Nonlinear Dissipation of Alfvén Waves
Alfvén waves are incompressible to first order and therefore believed to propagate without dissipating. A linearly polarised Alfvén wave is however compressible to second order due to the variations in magnetic pressure, B2/(2μ0), (e.g. Alfvén & Fälthammar 1963). The wave can therefore steepen to discontinuities (Cohen & Kulsrud 1974).