A. O. Smirnov, “Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves”, TMF, 173:1 (2012), 89–103; Theoret. and Math. Phys., 173:1 (2012), 1403

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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 173, Number 1, Pages 89–103
DOI: https://doi.org/10.4213/tmf6947 (Mi tmf6947)

This article is cited in 19 scientific papers (total in 19 papers)

Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves

A. O. Smirnov

St.~Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia

Full-text PDF (1215 kB) Citations (19)

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DOI: https://doi.org/10.4213/tmf6947

Abstract: We construct a family of two-gap solutions of the focusing nonlinear Schrödinger equation and derive a condition under which the solutions behave as the so-called freak waves located at the nodes of a two-dimensional lattice. We also study how the lattice parameters depend on the parameters of the spectral curve.

Keywords: rogue wave, freak wave, nonlinear Schrödinger equation, theta function, reduction, covering.

Received: 13.01.2012
Revised: 10.03.2012

English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 1, Pages 1403–1416
DOI: https://doi.org/10.1007/s11232-012-0122-6

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. O. Smirnov, “Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves”, TMF, 173:1 (2012), 89–103; Theoret. and Math. Phys., 173:1 (2012), 1403–1416

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Linking options:

https://www.mathnet.ru/eng/tmf6947

https://doi.org/10.4213/tmf6947

https://www.mathnet.ru/eng/tmf/v173/i1/p89

This publication is cited in the following 19 articles:

Ruomeng Li, Jingru Geng, Xianguo Geng, “Breather and rogue-wave solutions of the semi-discrete and continuous nonlinear Schrödinger equations on theta-function backgrounds”, Nonlinearity, 38:1 (2025), 015012
Natanael Karjanto, “Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation”, Mathematics, 12:5 (2024), 744
Liuyi Pan, Lei Wang, Lei Liu, Wenrong Sun, Xiaoxia Ren, “Non-degenerate localised waves beyond Manakov system and their new perspectives”, Nonlinearity, 37:10 (2024), 105016
A. O. Smirnov, V. B. Matveev, “Finite-gap solutions of nonlocal equations in Ablowitz-Kaup-Newell-Segur hierarchy”, Ufa Math. J., 13:2 (2021), 81–98
Pelinovsky D.E., “Instability of Double-Periodic Waves in the Nonlinear Schrodinger Equation”, Front. Physics, 9 (2021), 599146
V. B. Matveev, A. O. Smirnov, “Elliptic solitons and «freak waves»”, St. Petersburg Math. J., 33:3 (2022), 523–551
T. V. Redkina, O. V. Novikova, “Primenenie differentsialnykh svyazei Beklunda dlya postroeniya tochnykh reshenii nelineinykh giperbolicheskikh uravnenii”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2020, no. 3, 54–67
P. G. Grinevich, P. M. Santini, “The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes”, Russian Math. Surveys, 74:2 (2019), 211–263
Chen J. Pelinovsky D.E. White R.E., “Rogue Waves on the Double-Periodic Background in the Focusing Nonlinear Schrodinger Equation”, Phys. Rev. E, 100:5 (2019), 052219
Pierre GAİLLARD, “Differential Relations for the Solutions to the NLS Equation and Their Different Representations”, Communications in Advanced Mathematical Sciences, 2:4 (2019), 235
V. B. Matveev, A. O. Smirnov, “Two-phase periodic solutions to the AKNS hierarchy equations”, J. Math. Sci. (N. Y.), 242:5 (2019), 722–741
Bertrand Kibler, Shaping Light in Nonlinear Optical Fibers, 2017, 293
V. B. Matveev, A. O. Smirnov, “Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach”, Theoret. and Math. Phys., 186:2 (2016), 156–182
Zhao H.-H. Zhao X.-J. Guo R., “Periodic solutions, breathers and rogue waves in a generalized coupled Hirota system”, Optik, 127:20 (2016), 9295–9304
Aleksandr O. Smirnov, Sergei G. Matveenko, Sergei K. Semenov, Elena G. Semenova, “Three-Phase Freak Waves”, SIGMA, 11 (2015), 032, 14 pp.
Chabalko Ch. Moitra A. Balachandran B., “Rogue Waves: New Forms Enabled By Gpu Computing”, Phys. Lett. A, 378:32-33 (2014), 2377–2381
Dubinov A.E., Kitayev I.N., “Nonlinear Multiplicative Ion-Plasma Oscillations”, Phys. Wave Phenom., 22:1 (2014), 52–55
A. O. Smirnov, G. M. Golovachev, “Trekhfaznye resheniya nelineinogo uravneniya Shredingera v ellipticheskikh funktsiyakh”, Nelineinaya dinam., 9:3 (2013), 389–407
Priya N.V., Senthilvelan M., Lakshmanan M., “Akhmediev Breathers, Ma Solitons, and General Breathers From Rogue Waves: a Case Study in the Manakov System”, Phys. Rev. E, 88:2 (2013), 022918

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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