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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 204, Number 3, Pages 383–395
DOI: https://doi.org/10.4213/tmf9901
(Mi tmf9901)
 

This article is cited in 12 scientific papers (total in 12 papers)

Multiphase solutions of nonlocal symmetric reductions of equations of the AKNS hierarchy: General analysis and simplest examples

V. B. Matveevab, A. O. Smirnovc

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Institut de Mathématiques de Bourgogne, Université de Bourgogne — Franche Comté, Dijon, France
c St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia
References:
Abstract: We consider nonlocal symmetries that all or all even (all odd) equations of the AKNS hierarchy have. We construct examples of solutions simultaneously satisfying several nonlocal equations of the AKNS hierarchy. We present a detailed study of single-phase solutions.
Keywords: PT symmetry, nonlocal model, AKNS hierarchy, nonlinear Schrödinger equation, modified Korteweg–de Vries equation.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00734
This research was supported by the Russian Foundation for Basic Research (Grant No. 19-01-00734).
Received: 09.03.2020
Revised: 11.04.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 204, Issue 3, Pages 1154–1165
DOI: https://doi.org/10.1134/S0040577920090056
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. B. Matveev, A. O. Smirnov, “Multiphase solutions of nonlocal symmetric reductions of equations of the AKNS hierarchy: General analysis and simplest examples”, TMF, 204:3 (2020), 383–395; Theoret. and Math. Phys., 204:3 (2020), 1154–1165
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9901
  • https://www.mathnet.ru/eng/tmf/v204/i3/p383
  • This publication is cited in the following 12 articles:
    1. In-Di Lyu, Chzhun-Lun Chzhao, “Volny-ubiitsy (2+1)-mernogo integriruemogo nelokalnogo uravneniya Shredingera s obrascheniem prostranstva-vremeni”, TMF, 222:1 (2025), 41–61  mathnet  crossref
    2. A. B. Khasanov, T. G. Khasanov, “The Cauchy Problem for the Nonlinear Complex Modified Korteweg-de Vries Equation with Additional Terms in the Class of Periodic Infinite-Gap Functions”, Sib Math J, 65:4 (2024), 846  crossref
    3. A. B. Khasanov, T. G. Khasanov, “Zadacha Koshi dlya nelineinogo kompleksnogo modifitsirovannogo uravneniya Kortevega — de Friza (kmKdF) s dopolnitelnymi chlenami v klasse periodicheskikh beskonechnozonnykh funktsii”, Sib. matem. zhurn., 65:4 (2024), 735–759  mathnet  crossref
    4. A. Khasanov, R. Eshbekov, Kh. Normurodov, “Integration of a nonlinear Hirota type equation with finite density in the class of periodic functions”, Lobachevskii J. Math., 44:10 (2023), 4329  crossref  mathscinet
    5. J. Wang, H. Wu, “On (2+1)-dimensional mixed AKNS hierarchy”, Commun. Nonlinear Sci. Numer. Simul., 104 (2022), 106052  crossref  mathscinet  isi
    6. G. A. Mannonov, A. B. Khasanov, “The Cauchy problem for a nonlinear Hirota equation in the class of periodic infinite-zone functions”, St. Petersburg Math. J., 34:5 (2023), 821–845  mathnet  crossref
    7. A. Boutet de Monvel, Y. Rybalko, D. Shepelsky, “Focusing nonlocal nonlinear Schrödinger equation with asymmetric boundary conditions: large-time behavior”, Toeplitz Operators and Random Matrices, Operator Theory: Advances and Applications, 289, 2022, 193  crossref
    8. J. Wang, H. Wu, D.-J. Zhang, “Reciprocal transformations of the space–time shifted nonlocal short pulse equations”, Chinese Phys. B, 31:12 (2022), 120201  crossref
    9. V. S. Gerdjikov, A. O. Smirnov, “Fundamental analytic solutions for the Kulish-Sklyanin model with constant boundary conditions”, APplication of Mathematics in Technical and Natural Sciences: 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'21, AIP Conf. Proc., 2522, no. 1, 2022, 030004  crossref
    10. S.-m. Liu, J. Wang, D.-j. Zhang, “Solutions to integrable space-time shifted nonlocal equations”, Reports on Mathematical Physics, 89:2 (2022), 199  crossref  mathscinet
    11. 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  mathnet  crossref  isi
    12. V. B. Matveev, A. O. Smirnov, “Elliptic solitons and «freak waves»”, St. Petersburg Math. J., 33:3 (2022), 523–551  mathnet  crossref
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