About scattered field's singularities and Rayleigh hypothesis

The new vision on the Rayleigh hypothesis is discussed based on several new results of computer simulations. Possible or actual singularities in the analytic continuation of the scattering problem solutions for the two and tree dimensional Helmholtz equation are studied in order to investigate the Rayleigh hypothesis validity. The procedure uses computer simulations for the solution particular problems, and relates to the several types of singularities, associated with the elementary source as well as boundary curve's singularities in the solution. The results provide confirmation of criteria for the validity of the Rayleigh hypothesis that have been criticized by several investigators, including us. In this paper it is demonstrated, that the Rayleigh hypothesis might be correct and has deep physical meaning.