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

✍ Scribed by Partha Guha; A. Ghose Choudhury

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 243 KB
• Volume: 16
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2010.11.016

✦ Synopsis

of calculus of variations Lagrangian Jacobi last multiplier Jacobi-Ostrogradski's method a b s t r a c t

We derive the Lagrangians of the reduced fourth-order ordinary differential equations studied by Kudryashov, when they satisfy the conditions stated by Fels [Fels ME, The inverse problem of the calculus of variations for scalar fourth-order ordinary differential equations. Trans Am Math Soc 1996;348:5007-29] using Jacobi's last multiplier technique. In addition the Hamiltonians of these equations are derived via Jacobi-Ostrogradski's theory. In particular, we compute the Lagrangians and Hamiltonians of fourth-order Kudryashov equations which pass the Painlevé test.