Riccati parametric deformations of the Cornu spiral

Abstract

"In this article, a parametric deformation of the Cornu spiral is introduced. The parameter is an integration constant which appears in the general solution of the Riccati equation and is related to the Fresnel integrals. The Argand plots of the deformed spirals are presented and a supersymmetric (Darboux) structure of the deformation is revealed through the factorization approach."