Existence of subsonic periodic traveling waves in discrete Klein-Gordon type equations with nonlocal interaction

Authors

DOI:

https://doi.org/10.31652/3041-1955/2024-01-02-01

Keywords:

subsonic periodic traveling waves, Klein-Gordon type equations, nonlocal interaction, critical points, linking theorem

Abstract

The article deals with the discrete Klein-Gordon type equations that describe infinite chains of linearly coupled nonlinear oscillators with nonlocal interactions. It is assumed that each oscillator interacts with several of its neighbors on both sides. The main result concerns the existence of subsonic periodic traveling wave solutions in such equations. Sufficient conditions for the existence of such waves are established using the variational method and the linking theorem.

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Author Biographies

  • Serhii Bak, Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University
    Serhii Bak, Doctor of Science in Physіcs and Mathematics, Professor, Department of Mathematics and Informatics, Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, 32 Ostrozkyi Str., Vinnytsia 21001, Ukraine.
  • Halyna Kovtoniuk, Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University
    Halyna Kovtoniuk, Candidate of Science in Pedagogy, Associate Professor, Department of Mathematics and Informatics, Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, 32 Ostrozkyi Str., Vinnytsia 21001, Ukraine.

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Published

2024-10-17

Issue

Vol. 1 No. 2 (2024)

Section

Actual problems of mathematics

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Copyright (c) 2024 Сергій Бак, Галина Ковтонюк

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Existence of subsonic periodic traveling waves in discrete Klein-Gordon type equations with nonlocal interaction. (2024). Mathematics, Informatics, Physics: Science and Education, 1(2), 99-110. https://doi.org/10.31652/3041-1955/2024-01-02-01