A Wigner approximation method for wave propagation

An approximation method for pulse propagation based on the Wigner position-wavenumber representation is presented. The method is very easy to apply and moreover is physically illuminating. One obtains the evolved approximate Wigner distribution from the initial Wigner distribution by a simple linear translation in phase space. Each phase space point propagates at constant velocity given by the group velocity at the phase space point. Dissipative propagation (damping) is also taken into account. From the approximate Wigner distribution, one can obtain the approximate magnitude of the evolved pulse and the approximate local wavenumber, that is, the spatial derivative of the phase of the pulse. Examples are given to illustrate the method.