## 4. Linear wave equationIn order to gain some understanding on the properties of nonlinear fast magnetosonic waves, we consider the following expression governing the propagation of fast waves in the linear regime (cf. Oliver et al. 1993), where and are given by expressions (11) and (8), respectively. Note that after taking , the `force' on the
right-hand side of this expression lies in the normal direction (to
the equilibrium Moreover, Eq. (15) multiplied by reduces to where the Laplacian operator on the right-hand side indicates that the magnetic pressure gradient is responsible for the propagation of fast MHD perturbances in the present model. Following
ade
& Ballester (1995b), analytical solutions to Eq. (16) with
are obtained for the variable where is the normal velocity component. In
terms of which can be solved analytically using Fourier transformation techniques once the initial velocity and its time derivative are imposed. The function follows from the expression with and © European Southern Observatory (ESO) 1998 Online publication: January 16, 1998 |