On Bäcklund transformations to stationary equations in hierarchy of the second Painlevé equation
https://doi.org/10.29235/1561-2430-2024-60-3-195-202
Abstract
The analytical properties of solutions to stationary equations of the second and fourth orders in the hierarchy of the second Painlevé equation are considered. For the second-order equation, it is shown that the Bäcklund transformation in the general case determines the formula of the addition theorem for the Weierstrass elliptic function. For the fourth and sixth-order equations, Bäcklund transformations and special classes of solutions are constructed. It has been established that, for a certain relationship between the parameters, the set of solutions to the first term of the stationary hierarchy is a subset of solutions to the second term and the set of solutions to the second term of the hierarchy is a subset of solutions of the six-order equation of the stationary hierarchy of the second Painlevé equation.
About the Author
V. I. Gromak
Belarusian State University
Belarus
Belarus
Valery I. Gromak – Dr. Sc. (Physics and Mathematics), Professor, Department of Differential Equations and Systems Analysis
4, Nezavisimosti Ave., 220030, Minsk
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