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      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/026/02/0257-0274

    • Keywords

       

      Continuum mechanics, fields, linear wave equation, Lax pair, KdV equation, conserved quantities, zero curvature representation, monodromy matrix.

    • Abstract

       

      In Part I [1], we introduced the idea of a Lax pair and ex-plained how it could be used to obtain conserved quantities for systems of particles. Here, we extend these ideas to continuum mechanical systems of fields such as the linear wave equation for vibrations of a stretched string and the Kortewegde Vries (KdV) equation for water waves. Unlike the Lax matrices for systems of particles, here Lax pairs are differential operators. A key idea is to view the Lax equation as a compatibility condition between a pair of linear equations. This is used to obtain a geometric reformulation of the Lax equation as the condition for a certain curvature to vanish. This ‘zero curvature representation’ then leads to a recipe for finding (typically an infinite sequence of) conserved quantities.

    • Author Affiliations

       

      Govind S Krishnaswami1 T R Vishnu 1

      1. Chennai Mathematical Institute H1 SIPCOT IT Park Siruseri, Kelambakkam 603 103 Tamil Nadu.
    • Dates

       
  • Resonance – Journal of Science Education | News

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