Revisiting Separation of Variables in Hamilton-Jacobi Equations: Abstract and Introduction

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A critical examination of recent claims regarding separation of variables in Hamilton-Jacobi equations, clarifying misconceptions and historical contributions.
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This article is a feedback on an article by M.O. Katanaev in Physica Scripta (2023, 98, 104001) The author sets out his vision of the history of the creation of the theory of complete separation of variables in the free Hamilton-Jacobi equation. He claims that the results obtained in the articles significantly complement the theory. For the first time an explicit form of integrals of motion has been found.