Fractional Darboux Transformations

Details Fractional Darboux Transformations Fractional Darboux Transformations

2002-02-13

arxiv.org/abs/math-ph/0202020v2

Physics

Mathematical Physics

15 pages,submitted N.C. B corrected some typos added two references

Scientific paper

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.

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