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Abstract
The main objective of this paper is to study the properties of the Bäcklund transformations and the auto‐Bäcklund transformations, to construct the nonlinear superposition formulas for the solutions of the fifth Painlevé equation and to obtain the values of the parameters after the successive application of the Bäcklund transformations.
Darbe nagrinejamos Backlund'o transformaciju siejamu su penktaja Penleve lygtimi, savybes. Remiantis šiomis savybemis sukonstruotos Penleve lygties sprendiniu netiesiogines superpozicijos. Tai suteikia galimybe sudaryti nagrinejamos lygties sprendiniu herarchija ir susieti ja su kitos lygties (su kitais parametrais) sprendiniais.