Topic of Research Seminar: Linearization of Nonlinear Ordinary Differential Equations: From Lie’s Classical Theory to Higher Order Generalizations via Point Transformations

Abstract: Nonlinear ordinary differential equations arise naturally in modeling real-world phenomena across physics, engineering, and biology, yet their exact solutions have long remained elusive. While approximation methods dominated early efforts, Sophus Lie’s profound discovery that symmetries govern the integrability of differential equations opened the door to exact linearization via invertible point transformations. In this talk we will explore Lie’s classical criteria for linearizing second-order scalar ODEs, including the celebrated Lie-Tressé conditions, and extend the discussion to Ibragimov’s systematic results for third- and higher-order equations. Through concrete examples and proofs, we’ll demonstrate how certain nonlinear equations can be precisely mapped to linear forms, revealing their hidden linear structure and yielding exact analytical solutions.

Subject Field of Topic: Symmetry Methods for Differential Equation

Name of Speaker: Ms. Kinza Iftikhar

Professorial Rank of Speaker: PhD Scholar (Mathematics Dpt.) School of Natural Sciences (SNS)

Email of Speaker: [email protected]

Affiliation of Speaker: School of Natural Sciences (SNS – NUST)

Date and Venue: (Wednesday) 24 December, 2025, 03:30 PM, Room # 403 Old Building, School of Natural Sciences (SNS), NUST Islamabad