• The Idea of a Lax Pair–Part I: Conserved Quantities for a Dynamical System

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/025/12/1705-1720

    • Keywords

       

      Dynamical systems, conserved quantities, Lax pair, isospectral evolution, harmonic oscillator, Toda chain, Euler top.

    • Abstract

       

      Conserved quantities can help to understand and solve the equations of motion of various dynamical systems. Lax pairs are a useful tool to find conserved quantities of some dynami-cal systems. We give a motivated introduction to the idea of a Lax pair using examples such as the linear harmonic oscilla-tor, Toda chain and Eulerian rigid body. A key step is to write the equations in ‘Lax form’, which makes it easy to read off conserved quantities. In Part II, these ideas will be extended from systems of particles to continuum systems of fields and also given a geometric interpretation in terms of curvature..

    • Author Affiliations

       

      Govind Krishnaswami1 T R Vishnu1

      1. Chennai Mathematical Institute H1 SIPCOT IT Park Siruseri, Kelambakkam 603103 Tamil Nadu.
    • Dates

       

© 2021-2022 Indian Academy of Sciences, Bengaluru.