Solitary phase waves in a chain of autonomous oscillators
- In the present paper, we study phase waves of self-sustained oscillators with a nearest-neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics, we approximate the lattice with a quasi-continuum (QC). The resulting partial differential model is then further reduced to the Gardner equation, which predicts many properties of the underlying solitary structures. Using an iterative procedure on the original lattice equations, we determine the shapes of solitary waves, kinks, and the flat-like solitons that we refer to as flatons. Direct numerical experiments reveal that the interaction of solitons and flatons on the lattice is notably clean. All in all, we find that both the QC and the Gardner equation predict remarkably well the discrete patterns and their dynamics.
| Author details: | Philip RosenauORCiD, Arkadij PikovskijORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1063/1.5144939 |
| ISSN: | 1054-1500 |
| ISSN: | 1089-7682 |
| Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/32491900 |
| Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
| Publisher: | American Institute of Physics, AIP |
| Place of publishing: | Melville, NY |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/05/08 |
| Publication year: | 2020 |
| Release date: | 2023/09/27 |
| Volume: | 30 |
| Issue: | 5 |
| Article number: | 053119 |
| Number of pages: | 8 |
| Funding institution: | Laboratory of Dynamical Systems and Applications NRU HSE of the Ministry; of Science and Higher Education of Russian Federation [075-15-2019-1931] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
