TY  - JOUR
AU  - Yee, Tat-Leung 
PY  - 2011
TI  - A New Perturbative Approach in Nonlinear Singularity Analysis
JF  - Journal of Mathematics and Statistics
VL  - 7
IS  - 3
DO  - 10.3844/jmssp.2011.249.254
UR  - https://thescipub.com/abstract/jmssp.2011.249.254
AB  - 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.