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 PFMT, 2019, Issue 1(38), Pages 72–77 (Mi pfmt627)

MATHEMATICS

The first integrals and rational solutions of differential equations with a moving singular line

B. Zhang, Y. Chen, I. P. Martynov

Y. Kupala Grogno State University

Abstract: The nonlinear autonomous higher-order differential equations with a moving singular line are studied. The first integrals of the Chazy equation and some other equations with a moving singular line are obtained. Nonlinear differential equations, for which general solutions are rational solutions of equations with a moving singular line are obtained. It is shown that with the help of Bäcklund transformations, rational solutions of equations with a movable singular line can be transformed into each other. Nonlinear differential equations of the second or third degree with respect to the highest derivative are obtained, for which these rational solutions are general solutions.

Keywords: differential equations, resonances, rational solutions, first integrals, Bäcklund transform, movable singular line.

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UDC: 517

Citation: B. Zhang, Y. Chen, I. P. Martynov, “The first integrals and rational solutions of differential equations with a moving singular line”, PFMT, 2019, no. 1(38), 72–77

Citation in format AMSBIB
\Bibitem{ZhaCheMar19} \by B.~Zhang, Y.~Chen, I.~P.~Martynov \paper The first integrals and rational solutions of differential equations with a moving singular line \jour PFMT \yr 2019 \issue 1(38) \pages 72--77 \mathnet{http://mi.mathnet.ru/pfmt627}