Front propagation in non-homogeneous $ϕ^4$ model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918503690272768 |
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| author | Gatlik, Jacek Dobrowolski, Tomasz Lasa, Dominika Kevrekidis, Panayotis G. |
| author_facet | Gatlik, Jacek Dobrowolski, Tomasz Lasa, Dominika Kevrekidis, Panayotis G. |
| contents | We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $ϕ^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with modified dissipation. The propagating front is described in two ways: as a kink solution in an effectively unbounded domain, and as a half-kink in a finite system. The half-kink represents the decay of the unstable state $ϕ=0$ toward the true vacuum. We show that while the effective description based on the kink provides accurate results, applying a similar approach to the half-kink leads to significant deviations from the predictions of the field model. We then demonstrate that a consistent description does exist and propose a modified effective model which reproduces the field-theory results over a relatively broad range of parameters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15826 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Front propagation in non-homogeneous $ϕ^4$ model Gatlik, Jacek Dobrowolski, Tomasz Lasa, Dominika Kevrekidis, Panayotis G. Pattern Formation and Solitons High Energy Physics - Phenomenology We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $ϕ^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with modified dissipation. The propagating front is described in two ways: as a kink solution in an effectively unbounded domain, and as a half-kink in a finite system. The half-kink represents the decay of the unstable state $ϕ=0$ toward the true vacuum. We show that while the effective description based on the kink provides accurate results, applying a similar approach to the half-kink leads to significant deviations from the predictions of the field model. We then demonstrate that a consistent description does exist and propose a modified effective model which reproduces the field-theory results over a relatively broad range of parameters. |
| title | Front propagation in non-homogeneous $ϕ^4$ model |
| topic | Pattern Formation and Solitons High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2605.15826 |