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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 11 scientific papers (total in 11 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
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DOI: https://doi.org/10.4213/tmf9901
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: $\mathcal{PT}$ 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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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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