Transformations of ordinary differential equations via Darboux transformation technique (Q5942394)

Here, the author proposes a new approach for obtaining transformations of solutions to nonlinear ordinary differential equations representable as a compatibility condition on overdetermined linear systems. The author derives the transformations of solutions to the overdetermined linear systems in the framework of the Darboux transformation technique [\textit{V. B. Matveev} and \textit{M. A. Salle}, Darboux transformation and solutions. Berlin etc.: Springer-Verlag (1991; Zbl 0744.35045)].NEWLINENEWLINENEWLINEIn section 2, the author formulates the Lax pairs of ODEs under consideration. In section 3, he presents explicit formulae of the Darboux transformations and discusses their properties. In section 4, he gives asymptotic expansions of the singular point neighbourhood of the Lax pair solutions. These expansions are used to build the transformations of the ODEs on the basis of the DT formulae.