Eur. Phys. J. Plus (2018) 133: 184
https://doi.org/10.1140/epjp/i2018-12013-3

Regular Article

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

¹ Department of Mathematics, University of Gujrat, 50700, Punjab, Pakistan
² Department of Mathematics, COMSATS Institute of Information Technology, 43600, Attock, Pakistan
³ Department of Physics, COMSATS Institute of Information Technology, Islamabad, Pakistan
⁴ Department of Electrical Engineering, COMSATS Institute of Information Technology, 43600, Attock, Pakistan

^* e-mail: muhammad.asif@ciit-attock.edu.pk

Received: 28 January 2018
Accepted: 12 April 2018
Published online: 16 May 2018

Abstract

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.