High order Melnikov method: Pendulums

Ali Oksasoglu; Qiudong Wang

doi:10.1016/j.jde.2021.12.015

High order Melnikov method: Pendulums

Ali Oksasoglu
, Qiudong Wang

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

3 Scopus citations

Abstract

In this paper, we present an explicit integral formula for the high order Melnikov function D₁(t₀) for periodically perturbed pendulum equations. The acquired integral formula is then applied to a specific pendulum equation to offer an example of high frequency perturbation, of which the classical Melnikov function D₀(t₀) fails to dominate the higher order term εD₁(t₀).

Original language	English (US)
Pages (from-to)	176-208
Number of pages	33
Journal	Journal of Differential Equations
Volume	312
DOIs	https://doi.org/10.1016/j.jde.2021.12.015
State	Published - Mar 5 2022
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2021.12.015

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title = "High order Melnikov method: Pendulums",

abstract = "In this paper, we present an explicit integral formula for the high order Melnikov function D1(t0) for periodically perturbed pendulum equations. The acquired integral formula is then applied to a specific pendulum equation to offer an example of high frequency perturbation, of which the classical Melnikov function D0(t0) fails to dominate the higher order term εD1(t0).",

author = "Ali Oksasoglu and Qiudong Wang",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2022",

month = mar,

day = "5",

doi = "10.1016/j.jde.2021.12.015",

language = "English (US)",

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pages = "176--208",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - High order Melnikov method

T2 - Pendulums

AU - Oksasoglu, Ali

AU - Wang, Qiudong

PY - 2022/3/5

Y1 - 2022/3/5

N2 - In this paper, we present an explicit integral formula for the high order Melnikov function D1(t0) for periodically perturbed pendulum equations. The acquired integral formula is then applied to a specific pendulum equation to offer an example of high frequency perturbation, of which the classical Melnikov function D0(t0) fails to dominate the higher order term εD1(t0).

AB - In this paper, we present an explicit integral formula for the high order Melnikov function D1(t0) for periodically perturbed pendulum equations. The acquired integral formula is then applied to a specific pendulum equation to offer an example of high frequency perturbation, of which the classical Melnikov function D0(t0) fails to dominate the higher order term εD1(t0).

UR - https://www.scopus.com/pages/publications/85122132191

UR - https://www.scopus.com/pages/publications/85122132191#tab=citedBy

U2 - 10.1016/j.jde.2021.12.015

DO - 10.1016/j.jde.2021.12.015

M3 - Article

AN - SCOPUS:85122132191

SN - 0022-0396

VL - 312

SP - 176

EP - 208

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

High order Melnikov method: Pendulums

Abstract

ASJC Scopus subject areas

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