Lagrangians of Painleve equations

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In this article, we investigate Lagrangians of Painleve equations. As is well known, Painleve equations can be rewritten into Painleve systems which are Hamiltonian systems. So we have a simple question that Painleve equations have Euler-Lagrange equation forms or not. The answer is Yes. Painleve equations are themselves Euler-Lagrange equations. We prove this fact and give Lagrangians of Painleve equations.

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