An effective description of the impact of inhomogeneities on the movement of the kink front in 2+1 dimensions
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915148550111232 |
|---|---|
| author | Gatlik, Jacek Dobrowolski, Tomasz Kevrekidis, Panayotis G. |
| author_facet | Gatlik, Jacek Dobrowolski, Tomasz Kevrekidis, Panayotis G. |
| contents | In the present work we explore the interaction of a one-dimensional kink-like front of the sine-Gordon equation moving in 2-dimensional spatial domains. We develop an effective equation describing the kink motion, characterizing its center position dynamics as a function of the transverse variable. The relevant description is valid both in the Hamiltonian realm and in the non-conservative one bearing gain and loss. We subsequently examine a variety of different scenarios, without and with a spatially-dependent heterogeneity. The latter is considered both to be one-dimensional ($y$-independent) and genuinely two-dimensional. The spectral features and the dynamical interaction of the kink with the heterogeneity are considered and comparison with the effective quasi-one-dimensional description (characterizing the kink center as a function of the transverse variable) is also provided. Generally, good agreement is found between the analytical predictions and the computational findings in the different cases considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17926 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An effective description of the impact of inhomogeneities on the movement of the kink front in 2+1 dimensions Gatlik, Jacek Dobrowolski, Tomasz Kevrekidis, Panayotis G. Pattern Formation and Solitons In the present work we explore the interaction of a one-dimensional kink-like front of the sine-Gordon equation moving in 2-dimensional spatial domains. We develop an effective equation describing the kink motion, characterizing its center position dynamics as a function of the transverse variable. The relevant description is valid both in the Hamiltonian realm and in the non-conservative one bearing gain and loss. We subsequently examine a variety of different scenarios, without and with a spatially-dependent heterogeneity. The latter is considered both to be one-dimensional ($y$-independent) and genuinely two-dimensional. The spectral features and the dynamical interaction of the kink with the heterogeneity are considered and comparison with the effective quasi-one-dimensional description (characterizing the kink center as a function of the transverse variable) is also provided. Generally, good agreement is found between the analytical predictions and the computational findings in the different cases considered. |
| title | An effective description of the impact of inhomogeneities on the movement of the kink front in 2+1 dimensions |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2310.17926 |