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

Partha Guha; A. Ghose Choudhury

doi:10.1016/j.cnsns.2010.11.016

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

Partha Guha, A. Ghose Choudhury

Mathematics

Surendranath College

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	British English
Pages (from-to)	3914-3922
Number of pages	9
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	16
Issue number	10
DOIs	https://doi.org/10.1016/j.cnsns.2010.11.016
State	Published - Oct 2011

Keywords

Fourth-order ordinary differential equations
Inverse problem of calculus of variations
Jacobi last multiplier
Jacobi-Ostrogradski's method
Lagrangian

Access to Document

10.1016/j.cnsns.2010.11.016

Cite this

@article{5dd6bb6dc4454fb99d188b0a00941e43,

title = "On Lagrangians and Hamiltonians of some fourth-order nonlinear Kudryashov ODEs",

abstract = "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 Painlev{\'e} test.",

keywords = "Fourth-order ordinary differential equations, Inverse problem of calculus of variations, Jacobi last multiplier, Jacobi-Ostrogradski's method, Lagrangian",

author = "Partha Guha and {Ghose Choudhury}, A.",

year = "2011",

month = oct,

doi = "10.1016/j.cnsns.2010.11.016",

language = "British English",

volume = "16",

pages = "3914--3922",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier B.V.",

number = "10",

}

TY - JOUR

T1 - On Lagrangians and Hamiltonians of some fourth-order nonlinear Kudryashov ODEs

AU - Guha, Partha

AU - Ghose Choudhury, A.

PY - 2011/10

Y1 - 2011/10

N2 - 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.

AB - 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.

KW - Fourth-order ordinary differential equations

KW - Inverse problem of calculus of variations

KW - Jacobi last multiplier

KW - Jacobi-Ostrogradski's method

KW - Lagrangian

UR - http://www.scopus.com/inward/record.url?scp=79955964086&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2010.11.016

DO - 10.1016/j.cnsns.2010.11.016

M3 - Article

AN - SCOPUS:79955964086

SN - 1007-5704

VL - 16

SP - 3914

EP - 3922

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 10

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this