On Lagrangians and Hamiltonians of some fourth-order nonlinear Kudryashov ODEs (Q634209)

\textit{N. A. Kudryashov} [J. Nonlinear Math. Phys. 8, Suppl., 172--177 (2001; Zbl 0982.34077)] considered two classes of fourth-order ODEs and applying the Painlevé test a number of remarkable subclasses is determined. The present paper uses the \textit{M. E. Fels} conditions of the inverse problem of variational calculus for fourth-order ODE from [Trans. Am. Math. Soc. 348, No. 12, 5007--5029 (1996; Zbl 0879.34016)] and a Jacobi last multiplier in order to derive Lagrangians for some Kudryashov equations. Also, with the well-known Ostrogradsky approach, the Hamiltonian form of these equations is expressed.