M. J. Ablowitz, Bao-Feng Feng, X. Luo, Z. Musslimani, “Inverse scattering transform for the nonlocal reverse space–time nonlinear Schrödinger equation”, TMF, 196:3 (2018), 343–372; Theoret. and Math. Phys., 196:3 (2018), 1241

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 343–372
DOI: https://doi.org/10.4213/tmf9449 (Mi tmf9449)

This article is cited in 56 scientific papers (total in 56 papers)

Inverse scattering transform for the nonlocal reverse space–time nonlinear Schrödinger equation

M. J. Ablowitz^a, Bao-Feng Feng^b, X. Luo^c, Z. Musslimani^d

^a Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO, USA
^b School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX, USA
^c Department of Mathematics, State University of New York at Buffalo, Buffalo, NY, USA
^d Department of Mathematics, Florida State University, Tallahassee, FL, USA

Full-text PDF (900 kB) Citations (56)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf9449

Abstract: Nonlocal reverse space–time equations of the nonlinear Schrödinger (NLS) type were recently introduced. They were shown to be integrable infinite-dimensional dynamical systems, and the inverse scattering transform (IST) for rapidly decaying initial conditions was constructed. Here, we present the IST for the reverse space–time NLS equation with nonzero boundary conditions (NZBCs) at infinity. The NZBC problem is more complicated because the branching structure of the associated linear eigenfunctions is complicated. We analyze two cases, which correspond to two different values of the phase at infinity. We discuss special soliton solutions and find explicit one-soliton and two-soliton solutions. We also consider spatially dependent boundary conditions.

Keywords: inverse scattering transform, nonlocal RST NLS equation.

Funding agency	Grant number
National Science Foundation	DMS-1310200 DMS-171599
National Natural Science Foundation of China	11728103
The research of M. J. Ablowitz was supported in part by the National Science Foundation (Grant No. DMS-1310200). The research of Bao-Feng Feng was supported in part by the National Science Foundation (Grant No. DMS-1715991) and NSFC for Overseas Scholar Collaboration Research (No. 11728103).

Received: 24.08.2017

English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 3, Pages 1241–1267
DOI: https://doi.org/10.1134/S0040577918090015

Bibliographic databases:

Document Type: Article

MSC: 37K15; 35Q51; 35Q15.

Language: Russian

Citation: M. J. Ablowitz, Bao-Feng Feng, X. Luo, Z. Musslimani, “Inverse scattering transform for the nonlocal reverse space–time nonlinear Schrödinger equation”, TMF, 196:3 (2018), 343–372; Theoret. and Math. Phys., 196:3 (2018), 1241–1267

Citation in format AMSBIB

\Bibitem{AblFenLuo18}

\by M.~J.~Ablowitz, Bao-Feng~Feng, X.~Luo, Z.~Musslimani

\paper Inverse scattering transform for the~nonlocal reverse space--time nonlinear Schr\"odinger equation

\jour TMF

\yr 2018

\vol 196

\issue 3

\pages 343--372

\mathnet{http://mi.mathnet.ru/tmf9449}

\crossref{https://doi.org/10.4213/tmf9449}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3849103}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...196.1241A}

\elib{https://elibrary.ru/item.asp?id=35410236}

\transl

\jour Theoret. and Math. Phys.

\yr 2018

\vol 196

\issue 3

\pages 1241--1267

\crossref{https://doi.org/10.1134/S0040577918090015}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000447277900001}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054665324}

Linking options:

https://www.mathnet.ru/eng/tmf9449

https://doi.org/10.4213/tmf9449

https://www.mathnet.ru/eng/tmf/v196/i3/p343

This publication is cited in the following 56 articles:

Tao Xu, Li‐Cong An, Min Li, Chuan‐Xin Xu, “N‐fold Darboux transformation of the discrete PT‐symmetric nonlinear Schrödinger equation and new soliton solutions over the nonzero background”, Stud Appl Math, 2024
Justin T Cole, Abdullah M Aurko, Ziad H Musslimani, “Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrödinger equations”, Nonlinearity, 37:4 (2024), 045001
H. I. Abdel-Gawad, Tukur Abdulkadir Sulaiman, Hajar F. Ismael, “Bright–dark envelope-optical solitons in space-time reverse generalized Fokas–Lenells equation: Modulated wave gain”, Mod. Phys. Lett. B, 2024
Lihan Zhang, Zhonglong Zhao, Yufeng Zhang, “Dynamics of transformed nonlinear waves for the (2+1)-dimensional pKP-BKP equation: interactions and molecular waves”, Phys. Scr., 99:7 (2024), 075220
Neja Prinsa N, E Parasuraman, Rishab Antosh B, Haci Mehmet Baskonus, A Muniyappan, “M-shaped, W-shaped and dark soliton propagation in optical fiber for nonlocal fourth order dispersive nonlinear Schrödinger equation under distinct conditions”, Phys. Scr., 99:10 (2024), 105205
Wen-Yu Zhou, Shou-Fu Tian, Zhi-Qiang Li, “On Riemann–Hilbert problem and multiple high-order pole solutions to the cubic Camassa–Holm equation”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2024, 1
H. Yang, R. Guo, “A study of periodic solutions and periodic background solutions for the reverse-space–time modified nonlinear Schrödinger equation”, Wave Motion, 117 (2023), 103112
T. Liu, T. Xia, “Riemann–Hilbert problems and N-soliton solutions of the nonlocal reverse space-time Chen–Lee–Liu equation”, Commun. Theor. Phys., 75:3 (2023), 035002
H. I. Abdel-Gawad, “Field and reverse field solitons in wave-operator nonlinear Schrödinger equation with space-time reverse: Modulation instability”, Commun. Theor. Phys., 75:6 (2023), 065005
V. M. Adukov, G. Mishuris, “Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method”, Proc. R. Soc. A, 479:2269 (2023)
X.-b. Xiang, S.-l. Zhao, Y. Shi, “Solutions and continuum limits to nonlocal discrete sine-Gordon equations: Bilinearization reduction method”, Stud. Appl. Math., 150:4 (2023), 1274
X. Wang, J. He, “Darboux transformation and general soliton solutions for the reverse space–time nonlocal short pulse equation”, Physica D: Nonlinear Phenomena, 446 (2023), 133639
X. Wu, S.-F. Tian, “On long-time asymptotics to the nonlocal short pulse equation with the Schwartz-type initial data: Without solitons”, Physica D: Nonlinear Phenomena, 448 (2023), 133733
M. Ozisik, A. Secer, M. Bayram, “(3+1)-dimensional Sasa–Satsuma equation under the effect of group velocity dispersion, self-frequency shift and self-steepening”, Optik, 275 (2023), 170609
Xiu-Bin Wang, Bo Han, “The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: Inverse scattering transform and multisoliton solutions”, Theoret. and Math. Phys., 210:1 (2022), 8–30
M. Gurses, A. Pekcan, “Soliton solutions of the shifted nonlocal NLS and MKdV equations”, Phys. Lett. A, 422 (2022), 127793
N. K. Vitanov, “Simple equations method (SEsM): an effective algorithm for obtaining exact solutions of nonlinear differential equations”, Entropy, 24:11 (2022), 1653
H. Zhou, Y. Chen, X. Tang, Y. Li, “Complex excitations for the derivative nonlinear Schrödinger equation”, Nonlinear Dyn, 109:3 (2022), 1947
X. Xin, Y. Xia, L. Zhang, H. Liu, “Bäcklund transformations, symmetry reductions and exact solutions of $(2+1)$ -dimensional nonlocal DS equations”, Applied Mathematics Letters, 132 (2022), 108157
W.-Q. Peng, Y. Chen, “ $N$ -double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann–Hilbert method and PINN algorithm”, Physica D: Nonlinear Phenomena, 435 (2022), 133274

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

Statistics & downloads:
Abstract page:	529
Full-text PDF :	111
References:	49
First page:	35

Registration to the website

Logotypes