Autonomous self-similar ordinary differential equations and the Painleve connection

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:328

Article

Andriopoulos, K. ; Leach, P. G. L.

关键词: Painleve;    integrability;    symmetry;   

DOI  :  10.1016/j.jmaa.2006.05.037

来源: Elsevier

【 摘 要 】

We demonstrate an intimate connection between nonlinear higher-order ordinary differential equations possessing the two symmetries of autonomy and self-similarity and the leading-order behaviour and resonances determined in the application of the Painleve Test. Similar behaviour is seen for systems of first-order differential equations. Several examples illustrate the theory. In an integrable case of the ABC system the Singularity analysis reveals a positive and a negative resonance and the method of leading-order behaviour leads naturally to a Laurent expansion containing both. (c) 2006 Elsevier Inc. All rights reserved.

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