Are Directed Waves Multifractal?

Wave propagation is studied in a sufficiently anisotropic random medium that backscattering along one direction can be neglected. A Fokker-Planck equation is derived the solution to which would provide a complete statistical description of such directed waves. The Fokker-Planck equation is mapped onto an su(1,1) ferromagnet and its symmetries are identified. Using the symmetries asymptotic wave function distributions are computed and used to show that directed wave functions fill space uniformly and do not have multifractal character.