Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.15806 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912283984134144 |
|---|---|
| author | Stefanov, Atanas G. Kevrekidis, P. G. |
| author_facet | Stefanov, Atanas G. Kevrekidis, P. G. |
| contents | In the present work we construct kink solutions for different (parabolic and wave) variants of the fractional $ϕ^4$ model, in both the sub-Laplacian and super-Laplacian setting. We establish existence and monotonicity results (for the sub - Laplacian case), along with sharp asymptotics which are corroborated through numerical computations. Importantly, in the sub-Laplacian regime, we provide the explicit and numerically verifiable spectral condition, which guarantees uniqueness for odd kinks. We check numerically the relevant condition to confirm the uniqueness of such solutions. In addition, we show asymptotic stability for the stationary kinks in the parabolic setting and also, the spectral stability for the traveling kinks in the corresponding wave equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kinks of fractional $ϕ^4$ models: existence, uniqueness, monotonicity, stability, and sharp asymptotics Stefanov, Atanas G. Kevrekidis, P. G. Analysis of PDEs Pattern Formation and Solitons In the present work we construct kink solutions for different (parabolic and wave) variants of the fractional $ϕ^4$ model, in both the sub-Laplacian and super-Laplacian setting. We establish existence and monotonicity results (for the sub - Laplacian case), along with sharp asymptotics which are corroborated through numerical computations. Importantly, in the sub-Laplacian regime, we provide the explicit and numerically verifiable spectral condition, which guarantees uniqueness for odd kinks. We check numerically the relevant condition to confirm the uniqueness of such solutions. In addition, we show asymptotic stability for the stationary kinks in the parabolic setting and also, the spectral stability for the traveling kinks in the corresponding wave equation. |
| title | Kinks of fractional $ϕ^4$ models: existence, uniqueness, monotonicity, stability, and sharp asymptotics |
| topic | Analysis of PDEs Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2503.15806 |