Self-similar halo modulation problem for weakly localized solutions

Consider weakly localized solutions and their stability analysis by the method of modulation equations. Let the halo part denote the component outside the core or localized part of the solution, and let a self-similar Ansatz impose self-similar scaling on that component. Self-similar halo problem. Study the stability of weakly localized solutions by extending the method of modulation equations to include the Ansatz that the halo part is self-similar. This is posed as a problem for future analysis rather than as an asserted result; the source does not state that such an extension has been carried out.