Rogue Waves in the Generalized Davey-Stewartson System

Mervenur Belin; Irma Hacinliyan

doi:10.1007/978-3-319-99719-3_52

Rogue Waves in the Generalized Davey-Stewartson System

Mervenur Belin, Irma Hacinliyan^*

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Technical University

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

Abstract

In this study, we consider rogue waves, which appear and disappear suddenly with large amplitudes, in the generalized Davey-Stewartson (GDS) system found in acoustics and discuss their dynamic structure. For the rogue wave solutions, we first obtain the Hirota bilinear form of the GDS system through rational and bilogarithmic transformations. Then, forming the solutions of the GDS system through determinants of matrices, we obtain three types of rogue wave solutions depending on the size of the matrices and the order of the N-rational solutions: fundamental (line), multi- and higher-order rogue waves. We report the behavior and differences of these three types of rogue waves and explain the change in the waves with respect to time.

Original language	English
Title of host publication	Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference
Editors	Herb Kunze, D. Marc Kilgour, Roman Makarov, Roderick Melnik, Xu Wang
Publisher	Springer New York LLC
Pages	579-589
Number of pages	11
ISBN (Print)	9783319997186
DOIs	https://doi.org/10.1007/978-3-319-99719-3_52
Publication status	Published - 2018
Event	International conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2017 - Waterloo, Canada Duration: 20 Aug 2017 → 25 Aug 2017

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	259
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2017
Country/Territory	Canada
City	Waterloo
Period	20/08/17 → 25/08/17

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

Keywords

Davey-Stewartson system
Rogue waves
Solution

Access to Document

10.1007/978-3-319-99719-3_52

Cite this

Belin, M., & Hacinliyan, I. (2018). Rogue Waves in the Generalized Davey-Stewartson System. In H. Kunze, D. M. Kilgour, R. Makarov, R. Melnik, & X. Wang (Eds.), Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference (pp. 579-589). (Springer Proceedings in Mathematics and Statistics; Vol. 259). Springer New York LLC. https://doi.org/10.1007/978-3-319-99719-3_52

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abstract = "In this study, we consider rogue waves, which appear and disappear suddenly with large amplitudes, in the generalized Davey-Stewartson (GDS) system found in acoustics and discuss their dynamic structure. For the rogue wave solutions, we first obtain the Hirota bilinear form of the GDS system through rational and bilogarithmic transformations. Then, forming the solutions of the GDS system through determinants of matrices, we obtain three types of rogue wave solutions depending on the size of the matrices and the order of the N-rational solutions: fundamental (line), multi- and higher-order rogue waves. We report the behavior and differences of these three types of rogue waves and explain the change in the waves with respect to time.",

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author = "Mervenur Belin and Irma Hacinliyan",

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Belin, M & Hacinliyan, I 2018, Rogue Waves in the Generalized Davey-Stewartson System. in H Kunze, DM Kilgour, R Makarov, R Melnik & X Wang (eds), Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference. Springer Proceedings in Mathematics and Statistics, vol. 259, Springer New York LLC, pp. 579-589, International conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2017, Waterloo, Canada, 20/08/17. https://doi.org/10.1007/978-3-319-99719-3_52

Rogue Waves in the Generalized Davey-Stewartson System. / Belin, Mervenur; Hacinliyan, Irma.
Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference. ed. / Herb Kunze; D. Marc Kilgour; Roman Makarov; Roderick Melnik; Xu Wang. Springer New York LLC, 2018. p. 579-589 (Springer Proceedings in Mathematics and Statistics; Vol. 259).

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

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Rogue Waves in the Generalized Davey-Stewartson System

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