Research Article Open Access

A New Perturbative Approach in Nonlinear Singularity Analysis

Tat-Leung Yee

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.

Journal of Mathematics and Statistics
Volume 7 No. 3, 2011, 249-254

DOI: https://doi.org/10.3844/jmssp.2011.249.254

Submitted On: 25 November 2010 Published On: 29 July 2011

How to Cite: Yee, T. (2011). A New Perturbative Approach in Nonlinear Singularity Analysis. Journal of Mathematics and Statistics, 7(3), 249-254. https://doi.org/10.3844/jmssp.2011.249.254

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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