P. G. Grinevich, P. M. Santini, “Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case”, TMF, 196:3 (2018), 404–418; Theoret. and Math. Phys., 196:3 (2018), 1294

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 3, Pages 404–418
DOI: https://doi.org/10.4213/tmf9544 (Mi tmf9544)

This article is cited in 13 scientific papers (total in 13 papers)

Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case

P. G. Grinevich^ab, P. M. Santini^cd

^a Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia
^b Lomonosov Moscow State University, Moscow, Russia
^c Dipartimento di Fisica, Università di Roma "La Sapienza", Roma, Italy
^d Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Roma, Italy

Full-text PDF (720 kB) Citations (13)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf9544

Abstract: Based on experimental observations of the recurrence of anomalous waves in water and nonlinear optics, we investigate the theory of anomalous waves for initial data almost satisfying the symmetry conditions in the experiment. We also derive useful formulas, in particular, describing the phase resonance in the recurrence, which can be compared with both the currently available experimental data and the experimental data to be obtained in the near future.

Keywords: focusing nonlinear Schrödinger equation, anomalous wave, recurrence, almost symmetric configuration, phase resonance.

Funding agency	Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations	0033-2018-0009
Instituto Nazionale di Fisica Nucleare
Sapienza Università di Roma	Ateneo 2017
The research of P. G. Grinevich was supported by FASO Russia (Project No. 0033-2018-0009) and the INFN Sezione di Roma and a Sapienza Ateneo 2017 Award Project.

Received: 12.02.2018
Revised: 23.02.2018

English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 3, Pages 1294–1306
DOI: https://doi.org/10.1134/S0040577918090040

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: P. G. Grinevich, P. M. Santini, “Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case”, TMF, 196:3 (2018), 404–418; Theoret. and Math. Phys., 196:3 (2018), 1294–1306

Citation in format AMSBIB

\Bibitem{GriSan18}

\by P.~G.~Grinevich, P.~M.~Santini

\paper Phase resonances of the~NLS rogue wave recurrence in the~quasisymmetric case

\jour TMF

\yr 2018

\vol 196

\issue 3

\pages 404--418

\mathnet{http://mi.mathnet.ru/tmf9544}

\crossref{https://doi.org/10.4213/tmf9544}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3849106}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...196.1294G}

\elib{https://elibrary.ru/item.asp?id=35410239}

\transl

\jour Theoret. and Math. Phys.

\yr 2018

\vol 196

\issue 3

\pages 1294--1306

\crossref{https://doi.org/10.1134/S0040577918090040}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000447277900004}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054696270}

Linking options:

https://www.mathnet.ru/eng/tmf9544

https://doi.org/10.4213/tmf9544

https://www.mathnet.ru/eng/tmf/v196/i3/p404

This publication is cited in the following 13 articles:

Yindi Liu, Zhonglong Zhao, “Rogue waves of the $(2+1)$ -dimensional integrable reverse space–time nonlocal Schrödinger equation”, Theoret. and Math. Phys., 222:1 (2025), 34–52
F Coppini, P M Santini, “Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz–Ladik lattices”, J. Phys. A: Math. Theor., 57:1 (2024), 015202
F Coppini, P M Santini, “The effect of loss/gain and Hamiltonian perturbations of the Ablowitz—Ladik lattice on the recurrence of periodic anomalous waves”, J. Phys. A: Math. Theor., 57:7 (2024), 075701
Liming Ling, Xuan Sun, “Elliptic-rogue waves and modulational instability in nonlinear soliton equations”, Phys. Rev. E, 109:6 (2024)
P. G. Grinevich, “Riemann Surfaces Close to Degenerate Ones in the Theory of Rogue Waves”, Proc. Steklov Inst. Math., 325 (2024), 86–110
F. Coppini, G. Grinevich, M. Santini, “Periodic Rogue waves and perturbation theory”, Encyclopedia of Complexity and Systems Science, 2022, 1–22
F. Coppini, G. Grinevich, M. Santini, “Periodic Rogue waves and perturbation theory”, Perturbation Theory, Encyclopedia of Complexity and Systems Science Series, 2022, 565
P. G. Grinevich, P. M. Santini, “The linear and nonlinear instability of the akhmediev breather”, Nonlinearity, 34:12 (2021), 8331–8358
F. Coppini, P. G. Grinevich, P. M. Santini, Encyclopedia of Complexity and Systems Science, 2021, 1
F. Coppini, P. G. Grinevich, P. M. Santini, “Effect of a small loss or gain in the periodic nonlinear Schrodinger anomalous wave dynamics”, Phys. Rev. E, 101:3 (2020), 032204
F. Coppini, P. M. Santini, “Fermi-Pasta-Ulam-Tsingou recurrence of periodic anomalous waves in the complex Ginzburg-Landau and in the Lugiato-Lefever equations”, Phys. Rev. E, 102:6 (2020), 062207
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
Santini P.M., “The Periodic Cauchy Problem For Pt-Symmetric Nls, i: the First Appearance of Rogue Waves, Regular Behavior Or Blow Up At Finite Times”, J. Phys. A-Math. Theor., 51:49 (2018), 495207

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

Statistics & downloads:
Abstract page:	500
Full-text PDF :	97
References:	51
First page:	17

Что такое QR-код?

Registration to the website

Logotypes