• Govind S Krishnaswami

      Articles written in Resonance – Journal of Science Education

    • The Idea of a Lax Pair–Part II: Continuum Wave Equations

      Govind S Krishnaswami T R Vishnu

      More Details Abstract Fulltext PDF

      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.

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