Double Alfvén waves

Abstract

We present ideas on nonlinear multiple waves in magnetohydrodynamics (MHD). In simple wave solutions, the dependent physical variables (the gas density, fluid velocity, magnetic field induction and gas pressure) depend on one phase variable which can be a function of the space and time variables (x, y, z, t). Double waves are another class of solutions that depend on two independent wave phases. As illustration of these ideas we present examples of double Alfvén waves. The solutions possess the usual integrals for Alfvén simple waves (the gas density, magnetic pressure, gas pressure and traveling wave velocity or group velocity), and have two independent phases. These waves may well be present in the solar wind. Double wave solutions, involving the other MHD wave modes are also possible.