On Bäcklund transformations to stationary equations in hierarchy of the second Painlevé equation
Year: 2024
Type: article
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.
Author: V. I. Gromak
Institution: Belarusian State University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403233796