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Teoreticheskaya i Matematicheskaya Fizika, 1988, Volume 74, Number 1, Pages 29–45 (Mi tmf4166)  

This article is cited in 71 scientific papers (total in 71 papers)

Exact integration of nonlinear Schrödinger equation

A. R. Its, A. V. Rybin, M. A. Sall'
References:
Abstract: The degeneracy of finite-gap expressions is used to obtain a manyparameter family of smooth periodic and almost periodic solutions of the nonlinear Schrödinger equation in terms of elementary functions. A scheme for obtaining these solutions by the Darboux transformation method is considered. Propagation of a soliton on an arbitrary background is studied.
Received: 04.06.1986
English version:
Theoretical and Mathematical Physics, 1988, Volume 74, Issue 1, Pages 20–32
DOI: https://doi.org/10.1007/BF01018207
Bibliographic databases:
Language: Russian
Citation: A. R. Its, A. V. Rybin, M. A. Sall', “Exact integration of nonlinear Schrödinger equation”, TMF, 74:1 (1988), 29–45; Theoret. and Math. Phys., 74:1 (1988), 20–32
Citation in format AMSBIB
\Bibitem{ItsRybSal88}
\by A.~R.~Its, A.~V.~Rybin, M.~A.~Sall'
\paper Exact integration of nonlinear Schr\"odinger equation
\jour TMF
\yr 1988
\vol 74
\issue 1
\pages 29--45
\mathnet{http://mi.mathnet.ru/tmf4166}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=940459}
\zmath{https://zbmath.org/?q=an:0678.35012}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 74
\issue 1
\pages 20--32
\crossref{https://doi.org/10.1007/BF01018207}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988P630800003}
Linking options:
  • https://www.mathnet.ru/eng/tmf4166
  • https://www.mathnet.ru/eng/tmf/v74/i1/p29
  • This publication is cited in the following 71 articles:
    1. 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  crossref
    2. Pierre Gaillard, “Rogue Waves in the Nonlinear Schrödinger, Kadomtsev–Petviashvili, Lakshmanan–Porsezian–Daniel and Hirota Equations”, Axioms, 14:2 (2025), 94  crossref
    3. A. O. Smirnov, “Konechnozonnye resheniya uravneniya mKdF: klassicheskaya i alternativnye formuly”, Algebra i analiz, 37:2 (2025), 156–176  mathnet
    4. Hui Yao, Hai-Qiang Zhang, Wei-Yue Xiong, “Breathers of Gerdjikov-Ivanov equation under background of elliptic function”, Acta Phys. Sin., 73:4 (2024), 040201  crossref
    5. 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  crossref
    6. Dmitry Agafontsev, Andrey Gelash, Stephane Randoux, Pierre Suret, “Multisoliton interactions approximating the dynamics of breather solutions”, Stud Appl Math, 152:2 (2024), 810  crossref
    7. 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  crossref
    8. 熊玮玥 Xiong Weiyue, 张海强 Zhang Haiqiang, 姚慧 Yao Hui, “AB系统在椭圆函数背景下的多呼吸子”, 光学学报, 44:5 (2024), 0519001  crossref
    9. Junchao Sun, Xiaoyan Tang, Yong Chen, “Exploring two-dimensional internal waves: A new three-coupled Davey–Stewartson system and physics-informed neural networks with weight assignment methods”, Physica D: Nonlinear Phenomena, 459 (2024), 134021  crossref
    10. Xi Zhang, Yu-Feng Wang, Sheng-Xiong Yang, “Breathers, rogue waves, and interaction solutions for the variable coefficient Kundu-nonlinear Schrödinger equation”, Physics of Fluids, 36:5 (2024)  crossref
    11. Pierre Gaillard, “From Algebro Geometric Solutions of the Toda Equation to Sato Formulas”, AppliedMath, 4:3 (2024), 856  crossref
    12. Yu-Shan Bai, Li-Na Zheng, Wen-Xiu Ma, Yin-Shan Yun, “Hirota Bilinear Approach to Multi-Component Nonlocal Nonlinear Schrödinger Equations”, Mathematics, 12:16 (2024), 2594  crossref
    13. P. G. Grinevich, “Riemann Surfaces Close to Degenerate Ones in the Theory of Rogue Waves”, Proc. Steklov Inst. Math., 325 (2024), 86–110  mathnet  crossref  crossref  zmath  isi
    14. G. U. Urazboev, M. M. Khasanov, A. K. Babadjanova, “Integration of the Negative Order Nonlinear Schrödinger Equation in the Class of Periodic Functions”, Lobachevskii J Math, 45:10 (2024), 5305  crossref
    15. Liming Ling, Xuan Sun, “The multi elliptic‐localized solutions and their asymptotic behaviors for the mKdV equation”, Stud Appl Math, 150:1 (2023), 135  crossref
    16. P. G. Grinevich, P. M. Santini, “The finite-gap method and the periodic Cauchy problem for $(2+1)$-dimensional anomalous waves for the focusing Davey–Stewartson $2$ equation”, Russian Math. Surveys, 77:6 (2022), 1029–1059  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    17. Mei Yang, Jian-Guo Liu, “Various dynamic behaviors to the (2+1)-dimensional Nizhnik–Novikov–Veselov equations in incompressible fluids”, Results in Physics, 40 (2022), 105880  crossref
    18. F. Coppini, P. G. Grinevich, P. M. Santini, Encyclopedia of Complexity and Systems Science Series, Perturbation Theory, 2022, 565  crossref
    19. F. Coppini, P. G. Grinevich, P. M. Santini, Encyclopedia of Complexity and Systems Science, 2022, 1  crossref
    20. Francesco Demontis, Cornelis van der Mee, “A Matrix Schrödinger Approach to Focusing Nonlinear Schrödinger Equations with Nonvanishing Boundary Conditions”, J Nonlinear Sci, 32:4 (2022)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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