Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in [Formula Presented] nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, “almost exact,” explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.