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

  • Levon A. Beklaryan
  • Armen L. BeklaryanEmail author
  • Alexander Yu. Gornov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)

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.

Keywords

Korteweg-de Vries equation Functional differential equations Traveling waves 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Central Economics and Mathematics Institute RASMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.Institute for System Dynamics and Control Theory of SB RASIrkutskRussia

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