Hamiltonians and conjugate Hamiltonians of some fourth-order nonlinear ODEs

Partha Guha, A. Ghose Choudhury, A. S. Fokas

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We first derive the Lagrangians of the reduced fourth-order ordinary differential equations studied by Kudryashov under the assumption that they satisfy the conditions stated by Fels [M.E. Fels, The inverse problem of the calculus of variations for scalar fourth-order ordinary differential equations, Trans. Amer. Math. Soc. 348, 1996, 50075029], using Jacobi's last multiplier technique. In addition we derive the Hamiltonians of these equations using the JacobiOstrogradski theory. Next, we derive the conjugate Hamiltonian equations for such fourth-order equations passing the Painlevé test. Finally, we investigate the conjugate Hamiltonian formulation of certain additional equations belonging to this family.

Original languageBritish English
Pages (from-to)2126-2138
Number of pages13
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number4
StatePublished - Mar 2012


  • Conjugate Hamiltonians
  • Fourth-order ordinary differential equations
  • Jacobi last multiplier
  • JacobiOstrogradski's method
  • Lagrangian


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