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- Title
On Bäcklund transformations for some second-order nonlinear differential equations.
- Authors
Tsegel'nik, V. V.
- Abstract
We obtain second-order nonlinear differential equations (and the associated Bäcklund transformations) with an arbitrary analytic function of the independent variable. These equations (which are not of Painlevé type in general) under certain constraints imposed on an arbitrary analytic function can be reduced, in particular, to the second, third or fourth Painlevé equation. We consider the properties of the Bäcklund transformations for the second-order nonlinear differential equations generated by two systems of two first-order nonlinear differential equations with quadratic nonlinearities in derivatives of the unknown functions.
- Subjects
NONLINEAR differential equations; BACKLUND transformations; DERIVATIVES (Mathematics); ANALYTIC functions; PAINLEVE equations
- Publication
Theoretical & Mathematical Physics, 2023, Vol 217, Issue 2, p1755
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577923110107