A review of specially discretized Klein-Gordon models

Yuri V. Bebikhov; Igor A. Shepelev; Sergey V. Dmitriev

doi:10.1117/12.2565763

9 April 2020 A review of specially discretized Klein-Gordon models

Yuri V. Bebikhov, Igor A. Shepelev, Sergey V. Dmitriev

Proceedings Volume 11459, Saratov Fall Meeting 2019: Computations and Data Analysis: from Nanoscale Tools to Brain Functions; 1145910 (2020) https://doi.org/10.1117/12.2565763
Event: Saratov Fall Meeting 2019: VII International Symposium on Optics and Biophotonics, 2019, Saratov, Russian Federation

Abstract

Discrete kinks in Klein-Gordon equations typically have two equilibrium configurations, an unstable one with maximum potential energy and a stable one with minimal energy. The difference between the kink energies in these two configurations gives the height of the Peierls-Nabarro potential. The maximal gradient of this potential gives the minimum force needed to set the kink in motion. It has been shown that some exceptional, non-integrable discretizations of the Klein-Gordon equation have zero static Peierls-Nabarro potential. An arbitrarily small external force in such models results in kink acceleration. Here several methods that give discrete Klein-Gordon models with zero static Peierls-Nabarro potential will be reviewed. Conservation laws which are satisfied for these discrete equations will be mentioned.

Citation Download Citation

Yuri V. Bebikhov, Igor A. Shepelev, and Sergey V. Dmitriev "A review of specially discretized Klein-Gordon models", Proc. SPIE 11459, Saratov Fall Meeting 2019: Computations and Data Analysis: from Nanoscale Tools to Brain Functions, 1145910 (9 April 2020); https://doi.org/10.1117/12.2565763

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