Fractional Darboux transformations
Abstract
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 ColeHopf 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.
 Publication:

Nuovo Cimento B Serie
 Pub Date:
 April 2002
 DOI:
 10.48550/arXiv.mathph/0202020
 arXiv:
 arXiv:mathph/0202020
 Bibcode:
 2002NCimB.117..449H
 Keywords:

 Mathematical Physics;
 Dynamical Systems
 EPrint:
 15 pages,submitted N.C. B corrected some typos added two references