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Periodic and soliton structures in a generalized Klein–Gordon equation with horizontal singular lines

Abstract

In this paper we give a detailed analysis on the existence of traveling wave (periodic) solutions to a generalized Klein–Gordon equation with a singular nonlinearity generated by two horizontal lines. In particular, we study some solutions that pass through (or meet) these singular lines. In this setting, we display some examples of new soliton structures.

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Acknowledgements

We would like to thank the referee for detailed comments on the manuscript and their suggestions to improve its readability.

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Correspondence to Manuel Zamora.

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Communicated by Adrian Constantin.

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Morales, N., Zamora, M. Periodic and soliton structures in a generalized Klein–Gordon equation with horizontal singular lines. Monatsh Math 196, 877–910 (2021). https://doi.org/10.1007/s00605-021-01626-5

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Keywords

  • Klein–Gordon equation
  • Horizontal singular lines
  • Traveling wave solutions
  • Periodic solutions
  • Soliton structures

Mathematics Subject Classification

  • 81Q05
  • 35C07
  • 35C08
  • 34C25