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We show that the Painleve equations P3-P5 can be derived (in a unified way)from a periodic sequence of Darboux transformations for a Schrodinger problemwith quadratic eigenvalue dependency. The general problem naturally dividesinto three different branches, each described by an infinite chain ofequations. The Painleve equations are obtained by closing the chainperiodically at the lowest nontrivial level(s). The chains provide ``symmetricforms'' for the Painleve equations, from which Hirota bilinear forms and Laxpairs are derived. In this paper (Part 1) we analyze in detail the cases P3-P5,while P6 will be studied in Part 2.Comment: 23 pages, 1 reference added + minor change

Painlevé equations from Darboux chains: I.PIII–PV

Painlevé equations from Darboux chains: I.P_III–P_V