On rational solutions of two differential equations with а moving singular line
https://doi.org/10.29235/1561-8323-2019-63-2-150-156
Abstract
The study is devoted to the analytical theory of ordinary differential equations. In the introduction, it is said that the object of investigation is nonlinear third-order autonomous differential equations with a moving singular line, and whose two-parameter rational solutions are known. The study aims to clarify how to obtain two-parameter rational solutions from the general solutions of these equations. In the analytical theory of differential equations, as a rule, nonlinear differential equations have negative resonances. Among these resonances is the resonance equal to –1 (trivial case). However, it is asserted in some of the researchers’ papers that the nature of these negative resonances has not been found until now. The equations only with non-trivial negative resonance arose the interest of researchers. And it appears that the rational solutions of
the equations can be constructed by their negative resonances. In this paper, a necessary and sufficient condition is indicated, at which the two-parameter rational solution of the equation with a moving singular line can be obtained from its general solution.
About the Authors
Bin-Bin Zhang
Yanka Kupala State University of Grodno.
Russian Federation
Russian Federation
Zhang Bin-bin - Postgraduate student.
22, Ozheshko Str., 230020, Grodno.
Yang Chen
Yanka Kupala State University of Grodno.
Russian Federation
Russian Federation
Chen Yang - Postgraduate student.
22, Ozheshko Str., 230020, Grodno.
I. P. Martynov
Yanka Kupala State University of Grodno.
Russian Federation
Russian Federation
Martynov Ivan Platonovich - D. Sc. (Physical and Mathematics), Professor.
22, Ozheshko Str., 230020, Grodno.
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