Mathematics, Informatics, Physics: Science and Education

Scientific journal

Vol. 1 No. 2 (2024)
Actual problems of mathematics

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

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  • Serhii Bak,
  • Halyna Kovtoniuk
Serhii Bak
Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University
Bio
Halyna Kovtoniuk
Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University
Bio

Published 2024-10-17

Keywords

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

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
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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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