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1 results

  • Partial Euler operators and the efficient inversion of Div

  • Part of
  • P. E. Hydon
  • Journal:
    European Journal of Applied Mathematics / Volume 34 / Issue 5 / October 2023
    Published online by Cambridge University Press:
    20 March 2023, pp. 1046-1066
    • Article
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  • The problem of inverting the total divergence operator is central to finding components of a given conservation law. This might not be taxing for a low-order conservation law of a scalar partial differential equation, but integrable systems have conservation laws of arbitrarily high order that must be found with the aid of computer algebra. Even low-order conservation laws of complex systems can be hard to find and invert. This paper describes a new, efficient approach to the inversion problem. Two main tools are developed: partial Euler operators and partial scalings. These lead to a line integral formula for the inversion of a total derivative and a procedure for inverting a given total divergence concisely.