A New Perturbative Approach in Nonlinear Singularity Analysis
Abstract
Problem statement: The study is devoted to the “mirror” method which enables one to study the integrability of nonlinear differential equations. Approach: A perturbative extension of the mirror method is introduced. Results: The mirror system and its first perturbation are then utilized to gain insights into certain nonlinear equations possessing negative Fuchs indices, which were poorly understood in the literatures. Conclusion/Recommendations: In particular, for a nonprincipal but maximal Painleve family the first-order perturbed series solution is already a local representation of the general solution, whose convergence can also be proved.
DOI: https://doi.org/10.3844/jmssp.2011.249.254
Copyright: © 2011 Tat-Leung Yee. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Mirror transformation
- painleve test
- singularity analysis
- Ordinary Differential Equations (ODE)
- singularity analysis
- mirror system
- maximal family
- perturbation expansion
- negative Fuchs indices