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- Title
Amalgamations of the Painlevé Equations.
- Authors
Kudryashov, N. A.
- Abstract
We present new hierarchies of nonlinear ordinary differential equations (ODEs) that are generalizations of the Painlevé equations. These hierarchies contain the Painlevé equations as special cases. We emphasize the sixth-order ODEs. Special solutions for one of them are expressed via the general solutions of the P1 and P2 equations and special cases of the P3 and P5 equations. Four of the six Painlevé equations can be considered special cases of these sixth-order ODEs. We give linear representations for solving the Cauchy problems for the hierarchy equations using the inverse monodromy transform.
- Subjects
PAINLEVE equations; NONLINEAR differential equations; BESSEL functions; MONODROMY groups; BESSEL polynomials; GROUP theory
- Publication
Theoretical & Mathematical Physics, 2003, Vol 137, Issue 3, p1703
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1023/B:TAMP.0000007918.94753.59