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Solutions of Traveling Wave Type for Korteweg-de Vries-Type System with Polynomial Potential

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Optimization and Applications (OPTIMA 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 974))

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Abstract

This paper deals with the implementation of numerical methods for searching for traveling waves for Korteweg-de Vries-type equations with time delay. Based upon the group approach, the existence of traveling wave solution and its boundedness are shown for some values of parameters. Meanwhile, solutions constructed with the help of the proposed constructive method essentially extend the class of systems, possessing solutions of this type, guaranteed by theory. The proposed method for finding solutions is based on solving a multiparameter extremal problem. Several numerical solutions are demonstrated.

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Acknowledgments

This work was partially supported by Russian Science Foundation, Project 17-71-10116. Also, the reported study was partially funded by RFBR according to the research project 16-01-00110 A.

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Authors and Affiliations

  1. Central Economics and Mathematics Institute RAS, Nachimovky prospect 47, 117418, Moscow, Russia

    Levon A. Beklaryan & Armen L. Beklaryan

  2. National Research University Higher School of Economics, Kirpichnaya Ulitsa 33, 105187, Moscow, Russia

    Armen L. Beklaryan

  3. Institute for System Dynamics and Control Theory of SB RAS, Lermontova street 134, 664033, Irkutsk, Russia

    Alexander Yu. Gornov

Authors
  1. Levon A. Beklaryan
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  2. Armen L. Beklaryan
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  3. Alexander Yu. Gornov
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Corresponding author

Correspondence to Armen L. Beklaryan .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Yury Evtushenko

  2. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  3. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  4. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Yury Kochetov

  5. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Mikhail Posypkin

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Beklaryan, L.A., Beklaryan, A.L., Gornov, A.Y. (2019). Solutions of Traveling Wave Type for Korteweg-de Vries-Type System with Polynomial Potential. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_21

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  • DOI: https://doi.org/10.1007/978-3-030-10934-9_21

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  • Print ISBN: 978-3-030-10933-2

  • Online ISBN: 978-3-030-10934-9

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