May Kink Solution to the Nonlinear Klein–Gordon Equation be Classified as a Soliton?
- Authors: Zav’yalov D.V.1, Konchenkov V.I.1, Kryuchkov S.V.1,2
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Affiliations:
- Volgograd State Technical University
- Volgograd State Social Pedagogical University
- Issue: Vol 64, No 10 (2019)
- Pages: 1391-1394
- Section: Theoretical and Mathematical Physics
- URL: https://journals.rcsi.science/1063-7842/article/view/204176
- DOI: https://doi.org/10.1134/S1063784219100256
- ID: 204176
Cite item
Abstract
Existence of the soliton solution to the generalized sine–Gordon equation (also known as the Kryuchkov–Kukhar’ equation) is numerically studied. The equation can be used to describe propagation of electromagnetic waves in a graphene-based superlattice. Calculation errors related to implicit representation of the kink solution to the equation under study are estimated. Variations in the shapes of kinks that move in opposite directions are studied prior to and after collision. The results show that the kink solution is not a soliton.
About the authors
D. V. Zav’yalov
Volgograd State Technical University
Email: svkruchkov@yandex.ru
Russian Federation, Volgograd, 400005
V. I. Konchenkov
Volgograd State Technical University
Email: svkruchkov@yandex.ru
Russian Federation, Volgograd, 400005
S. V. Kryuchkov
Volgograd State Technical University; Volgograd State Social Pedagogical University
Author for correspondence.
Email: svkruchkov@yandex.ru
Russian Federation, Volgograd, 400005; Volgograd, 400066