Amalgamations of the Painlevé Equations |
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Authors: | Kudryashov N A |
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Institution: | (1) Department of Applied Mathematics, Moscow Engineering and Physics Institute, 31 Kashirskoe Shosse, Moscow, 115409, Russia |
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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 P
1 and P
2 equations and special cases of the P
3 and P
5 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. |
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Keywords: | Painlevé equations Painlevé transcendents higher analogues isomonodromic linear problem |
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