Topic of Research Seminar: Noether Symmetries and First Integrals of EL-Equations

Abstract: The famous Noether’s theorem establishes an important connection between the conservation laws (first integrals) and symmetry properties of an Euler-Lagrange (EL) equation. The existence of a Noether symmetry of an EL-equation is essential from two aspects: first, it determines a conservation law (first integral) and, second, to reduce the order of underlying equation. The aim of the talk is to present an overview of Noether symmetries, finding associated first integrals (conservation laws) of single and systems of EL-equations and their use in writing down the solution of underlying equations or reduce via quadrature. We shall explore interesting properties of Noether symmetry operators by considering standard and nonstandard (alternative) Lagrangians of EL-equations and also discuss possible future research.

Subject Field of Topic: Applied Mathematics

Name of Speaker: Dr Muhammad Umar Farooq

Professorial Rank of Speaker: Associate Professor

University Email of Speaker: [email protected]

Affiliation of Speaker: College of Electrical & Mechanical Engineering, National University of Sciences & Technology (NUST), Islamabad

Date of Seminar: Monday 14 March, 2022