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Lax Representations in Classical Mechanics

      https://doi.org/10.1142/9789814282215_0008Cited by:0 (Source: Crossref)
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      Abstract:

      Let

      be an autonomous system of first-order ordinary differential equations. Assume that the functions Vk : ℝm → ℝ are smooth. Assume that this system can be written in the form (the so-called Lax representation)
      where A and L are n × n matrices and [A,L] ≡ AL − LA. Then the n × n matrices L and A are called a Lax pair…