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^*

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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.

Original language	English
Title of host publication	16th Chaotic Modeling and Simulation International Conference
Editors	Christos H. Skiadas, Yiannis Dimotikalis
Publisher	Springer Science and Business Media B.V.
Pages	175-190
Number of pages	16
ISBN (Print)	9783031609060
DOIs	https://doi.org/10.1007/978-3-031-60907-7_14
Publication status	Published - 2024
Event	16th Chaotic Modeling and Simulation International Conference, CHAOS 2023 - Crete, Greece Duration: 13 Jun 2023 → 17 Jun 2023

Publication series

Name	Springer Proceedings in Complexity
ISSN (Print)	2213-8684
ISSN (Electronic)	2213-8692

Conference

Conference	16th Chaotic Modeling and Simulation International Conference, CHAOS 2023
Country/Territory	Greece
City	Crete
Period	13/06/23 → 17/06/23

Bibliographical note

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

Keywords

Bifurcation
Generalized elastic medium
Nonlinear Schrödinger equation
Nonlinear wave propagation
Solitary wave solution

Access to Document

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

Cite this

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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",

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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).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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