Quantitative Stability of Two Weakly Interacting Kinks in the Stationary phi^6 Model
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914168625430528 |
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| author | Liao, Xin |
| author_facet | Liao, Xin |
| contents | We study the stationary phi^6 model given by the equation -phi''(x) + 2 phi(x) - 8 phi(x)^3 + 6 phi(x)^5 = 0 for x in R, and establish sharp quantitative stability estimates for configurations close to two weakly interacting kinks. More precisely, there exist constants a > 0 and epsilon > 0 such that, for any function u in L-infinity satisfying || u - H_{0,1}(x + x1) - H_{-1,0}(x + x2) ||_{H1} < epsilon with x2 - x1 > a, there exist constants y1, y2 such that || u - H_{0,1}(x + y1) - H_{-1,0}(x + y2) ||_{H1} + exp(-sqrt(2) (y2 - y1)) <= C * || u'' - 2 u + 8 u^3 - 6 u^5 ||_{L2}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative Stability of Two Weakly Interacting Kinks in the Stationary phi^6 Model Liao, Xin Analysis of PDEs 35B35, 35Q51, 35B40, 35Q53 We study the stationary phi^6 model given by the equation -phi''(x) + 2 phi(x) - 8 phi(x)^3 + 6 phi(x)^5 = 0 for x in R, and establish sharp quantitative stability estimates for configurations close to two weakly interacting kinks. More precisely, there exist constants a > 0 and epsilon > 0 such that, for any function u in L-infinity satisfying || u - H_{0,1}(x + x1) - H_{-1,0}(x + x2) ||_{H1} < epsilon with x2 - x1 > a, there exist constants y1, y2 such that || u - H_{0,1}(x + y1) - H_{-1,0}(x + y2) ||_{H1} + exp(-sqrt(2) (y2 - y1)) <= C * || u'' - 2 u + 8 u^3 - 6 u^5 ||_{L2}. |
| title | Quantitative Stability of Two Weakly Interacting Kinks in the Stationary phi^6 Model |
| topic | Analysis of PDEs 35B35, 35Q51, 35B40, 35Q53 |
| url | https://arxiv.org/abs/2511.18754 |