@article {10.3844/jmssp.2011.249.254,
article_type = {journal},
title = {A New Perturbative Approach in Nonlinear Singularity Analysis},
author = {Yee, Tat-Leung},
volume = {7},
year = {2011},
month = {Jul},
pages = {249-254},
doi = {10.3844/jmssp.2011.249.254},
url = {https://thescipub.com/abstract/jmssp.2011.249.254},
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 = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}