2002/02/13 by Mayer Humi, Humi, Mayer
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0202020
15 pages,submitted N.C. B corrected some typos added two references
arxiv created 2002/04/09 · arxiv updated 2009/11/30
In this paper we utilize the covariance of Ricatti equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of fractional Darboux transformations which can be recognized also as generalized Cole-Hopf transformations. We apply these transformations to find Schrodinger equations with isospectral potentials and to the linearization of some new classes of nonlinear partial differential equations.