A New Perturbative Approach in Nonlinear Singularity Analysis
DOI : 10.3844/jmssp.2011.249.254
Journal of Mathematics and Statistics
Volume 7, Issue 3
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.
© 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.