  We derive an approximate Gaussian solution of the Lindblad equation in the
semiclassical limit, given a general Hamiltonian and linear coupling with the
environment. The theory is carried out in the chord representation and
describes the evolved quantum characteristic function, which gives direct
access to the Wigner function and the position representation of the density
operator by Fourier transforms. The propagation is based on a system of
non-linear equations taking place in a double phase space, which coincides with
Heller's theory of unitary evolution of Gaussian wave packets when the
Lindbladian part is zero.
