title: Applying a Power Transformation to the Orbit of the 2nd Painleve Equation and Solving Differential Equations with Polynomial Right-hand Sides Via the 2nd Painleve Transcendent and in Polynomials
metadata.name: dc.contributor.author
metadata.value: Khakimova, Zilya Nailevna
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Timofeeva, Larisa Nikolaevna
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Atojan, Ajkanush Ashotovna
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-01-10T12:19:24Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-01-10T12:19:24Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-12
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2023.407
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44576
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The 2nd Painlevé equation is considered as a representative of the second-order class of ordinary differential equations (ODEs) with polynomial right-hand sides, as well as of the more general second-order class of equations with fractional polynomial right-hand sides. The second Painlevé equation with three terms on the right side has an orbit in the class of fractional polynomial equations with respect to the pseudogroup of the 36th order, and in the absence of the 3rd term – the 60th order. This paper presents a power transformation with an arbitrary parameter that preserves the polynomial or fractional polynomial form of the equations. This power-law transformation is applied to the orbital equations of the 2nd Painlevé equation with three and two terms on the right-hand sides of the equations. Pseudogroups of transformations induced by the above-mentioned pseudogroups of the 36th and 60th orders are constructed. All equations with one-constant arbitrariness corresponding to the vertices of the graphs of induced pseudogroups are found. General solutions of all found equations are obtained through the 2nd Painlevé transcendental or in polynomials. A theorem is presented that allows, using the scaling operation, to find general solutions to all the above equations with arbitrary coefficients.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Differential Equations and Control Processes;Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Ordinary differential equation (ODE) of the 2nd order
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: polynomial and fractional-polynomial differential equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: discrete transformation group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dihedral group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: pseudogroup of transformations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: 2nd Painlevé equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: 2nd Painlevé transcendent
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Applying a Power Transformation to the Orbit of the 2nd Painleve Equation and Solving Differential Equations with Polynomial Right-hand Sides Via the 2nd Painleve Transcendent and in Polynomials
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 142-154.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44576/1/142-154.pdf
resources.format: Adobe PDF
resources.size: 784,38 kB