A Higher-Order Septic Nonlinear Model for Transverse Waves in a Generalized Elastic Medium

Irma Hacinliyan

doi:10.1007/978-3-031-60907-7_14

A Higher-Order Septic Nonlinear Model for Transverse Waves in a Generalized Elastic Medium

Irma Hacinliyan^*

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Araştırma sonucu: Kitap/Rapor/Konferans Bildirisinde Bölüm › Konferans katkısı › bilirkişi

Özet

The nonlinear Schrödinger equation (NLSE) describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media such as elastic, acoustic, fluid, and fiber under different physical phenomena. It is clear that NLSEs are excellent examples of infinite-dimensional dynamical systems involving various and interesting scenarios; including soliton and wave packets; the existence of the homoclinic structure of solutions; so on. This study explores the contributions of the septic nonlinear and third-order dispersive effects in the nonlinear modulation of two transverse waves propagating in a generalized elastic medium. Using the reductive perturbation method, a pair of coupled quintic-septic NLSEs with a third-order dispersion term is obtained. Exact solutions and bifurcations of the new coupled system are also discussed.

Orijinal dil	İngilizce
Ana bilgisayar yayını başlığı	16th Chaotic Modeling and Simulation International Conference
Editörler	Christos H. Skiadas, Yiannis Dimotikalis
Yayınlayan	Springer Science and Business Media B.V.
Sayfalar	175-190
Sayfa sayısı	16
ISBN (Basılı)	9783031609060
DOI'lar	https://doi.org/10.1007/978-3-031-60907-7_14
Yayın durumu	Yayınlandı - 2024
Etkinlik	16th Chaotic Modeling and Simulation International Conference, CHAOS 2023 - Crete, Greece Süre: 13 Haz 2023 → 17 Haz 2023

Yayın serisi

Adı	Springer Proceedings in Complexity
ISSN (Basılı)	2213-8684
ISSN (Elektronik)	2213-8692

???event.eventtypes.event.conference???

???event.eventtypes.event.conference???	16th Chaotic Modeling and Simulation International Conference, CHAOS 2023
Ülke/Bölge	Greece
Şehir	Crete
Periyot	13/06/23 → 17/06/23

Bibliyografik not

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Belgeye Erişim

10.1007/978-3-031-60907-7_14

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

@inproceedings{e36719b7a48c4c3bad375868d3fa55dc,

title = "A Higher-Order Septic Nonlinear Model for Transverse Waves in a Generalized Elastic Medium",

abstract = "The nonlinear Schr{\"o}dinger equation (NLSE) describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media such as elastic, acoustic, fluid, and fiber under different physical phenomena. It is clear that NLSEs are excellent examples of infinite-dimensional dynamical systems involving various and interesting scenarios; including soliton and wave packets; the existence of the homoclinic structure of solutions; so on. This study explores the contributions of the septic nonlinear and third-order dispersive effects in the nonlinear modulation of two transverse waves propagating in a generalized elastic medium. Using the reductive perturbation method, a pair of coupled quintic-septic NLSEs with a third-order dispersion term is obtained. Exact solutions and bifurcations of the new coupled system are also discussed.",

keywords = "Bifurcation, Generalized elastic medium, Nonlinear Schr{\"o}dinger equation, Nonlinear wave propagation, Solitary wave solution",

author = "Irma Hacinliyan",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 16th Chaotic Modeling and Simulation International Conference, CHAOS 2023 ; Conference date: 13-06-2023 Through 17-06-2023",

year = "2024",

doi = "10.1007/978-3-031-60907-7\_14",

language = "English",

isbn = "9783031609060",

series = "Springer Proceedings in Complexity",

publisher = "Springer Science and Business Media B.V.",

pages = "175--190",

editor = "Skiadas, \{Christos H.\} and Yiannis Dimotikalis",

booktitle = "16th Chaotic Modeling and Simulation International Conference",

address = "Germany",

}

Hacinliyan, I 2024, A Higher-Order Septic Nonlinear Model for Transverse Waves in a Generalized Elastic Medium. in CH Skiadas & Y Dimotikalis (eds), 16th Chaotic Modeling and Simulation International Conference. Springer Proceedings in Complexity, Springer Science and Business Media B.V., pp. 175-190, 16th Chaotic Modeling and Simulation International Conference, CHAOS 2023, Crete, Greece, 13/06/23. https://doi.org/10.1007/978-3-031-60907-7_14

A Higher-Order Septic Nonlinear Model for Transverse Waves in a Generalized Elastic Medium. / Hacinliyan, Irma.
16th Chaotic Modeling and Simulation International Conference. ed. / Christos H. Skiadas; Yiannis Dimotikalis. Springer Science and Business Media B.V., 2024. p. 175-190 (Springer Proceedings in Complexity).

Araştırma sonucu: Kitap/Rapor/Konferans Bildirisinde Bölüm › Konferans katkısı › bilirkişi

TY - GEN

T1 - A Higher-Order Septic Nonlinear Model for Transverse Waves in a Generalized Elastic Medium

AU - Hacinliyan, Irma

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - The nonlinear Schrödinger equation (NLSE) describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media such as elastic, acoustic, fluid, and fiber under different physical phenomena. It is clear that NLSEs are excellent examples of infinite-dimensional dynamical systems involving various and interesting scenarios; including soliton and wave packets; the existence of the homoclinic structure of solutions; so on. This study explores the contributions of the septic nonlinear and third-order dispersive effects in the nonlinear modulation of two transverse waves propagating in a generalized elastic medium. Using the reductive perturbation method, a pair of coupled quintic-septic NLSEs with a third-order dispersion term is obtained. Exact solutions and bifurcations of the new coupled system are also discussed.

AB - The nonlinear Schrödinger equation (NLSE) describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media such as elastic, acoustic, fluid, and fiber under different physical phenomena. It is clear that NLSEs are excellent examples of infinite-dimensional dynamical systems involving various and interesting scenarios; including soliton and wave packets; the existence of the homoclinic structure of solutions; so on. This study explores the contributions of the septic nonlinear and third-order dispersive effects in the nonlinear modulation of two transverse waves propagating in a generalized elastic medium. Using the reductive perturbation method, a pair of coupled quintic-septic NLSEs with a third-order dispersion term is obtained. Exact solutions and bifurcations of the new coupled system are also discussed.

KW - Bifurcation

KW - Generalized elastic medium

KW - Nonlinear Schrödinger equation

KW - Nonlinear wave propagation

KW - Solitary wave solution

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DO - 10.1007/978-3-031-60907-7_14

M3 - Conference contribution

AN - SCOPUS:85218025305

SN - 9783031609060

T3 - Springer Proceedings in Complexity

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BT - 16th Chaotic Modeling and Simulation International Conference

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