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.
Penktosios Penlevé lygties Bäcklund'o transformacijos ir jų pritaikymai
Santrauka. Darbe nagrinėjamos Bäcklund‘o transformacijų siejamų su penktąja Penlevé lygtimi, savybės. Remiantis šiomis savybėmis sukonstruotos Penlevé lygties sprendinių netiesioginės superpozicijos. Tai suteikia galimybę sudaryti nagrinėjamos lygties sprendinių herarchiją ir susieti ją su kitos lygties (su kitais parametrais) sprendiniais.
Gromak, V., & Filipuk, G. (2001). The Bäcklund transformations of the fifth Painlevé equation and their applications. Mathematical Modelling and Analysis, 6(2), 221-230. https://doi.org/10.3846/13926292.2001.9637161
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