Two-dimensional shear Alfvén-wave turbulence in a plasma with arbitrary β

Two-dimensional shear Alfvén-wave turbulence is investigated for a plasma with arbitrary β value. A set of three equations, which reduces to the derivative nonlinear Schrödinger equation in the limit of parallel propagation, is derived. The genuinely two-dimensional case is governed by two coupled equations. For a non-parallel one-dimensional space dependence, the nonlinearity is shown to vanish to all orders.