On Some Particular Solutions of Factorizing Chains

In some cases, the study of factorizing chains encountered in the investigation of self-similar potentials and coherent states of quantum mechanics can be reduced to the investigation of nonlinear functional-differential equations of neutral type with linear deviations of the argument. We obtain new particular solutions of these equations and study their asymptotic properties. In addition, we find new particular solutions of the indicated factorizing chains and investigate some properties of these chains.