A new perturbative approach in nonlinear singularity analysis

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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. Copyright © 2011 Science Publications.
Original languageEnglish
Pages (from-to)249-254
JournalJournal of Mathematics and Statistics
Volume7
Issue number3
DOIs
Publication statusPublished - 2011

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Singularity Analysis
Nonlinear Analysis
Mirror
Series Solution
Painlevé
General Solution
Nonlinear Differential Equations
Integrability
Recommendations
Nonlinear Equations
First-order
Perturbation

Citation

Yee, T.-L. (2011). A new perturbative approach in nonlinear singularity analysis. Journal of Mathematics and Statistics, 7(3), 249-254.

Keywords

  • Mirror transformation
  • Painleve test
  • Singularity analysis
  • Ordinary Differential Equations (ODE)
  • Mirror system
  • Maximal family
  • Perturbation expansion
  • Negative Fuchs indices