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arXiv · 1801.04769

Nonlocal Representation of the $sl(2,R)$ Algebra for the Chazy equation

Andronikos Paliathanasis·Sameerah Jamal·P. G. L. Leach
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Abstract

A demonstration of how the point symmetries of the Chazy Equation become nonlocal symmetries for the reduced equation is discussed. Moreover we construct an equivalent third-order differential equation which is related to the Chazy Equation under a generalized transformation, and find the point symmetries of the Chazy Equation are generalized symmetries for the new equation. With the use of singularity analysis and a simple coordinate transformation we construct a solution for the Chazy Equation which is given by a Right Painlev\'e Series. The singularity analysis is applied to the new third-order equation and we find that it admits two solutions, one given by a Left Painlev\'e Series and one given by a Right Painlev\'e Series where the leading-order behaviors and the resonances are explicitly those of the Chazy Equation.

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BibTeXRIS

Andronikos Paliathanasis, Sameerah Jamal, P. G. L. Leach. 2018-01-15. Nonlocal Representation of the $sl(2,R)$ Algebra for the Chazy equation. https://arxiv.org/abs/1801.04769

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