Radiation damping of the soliton internal mode in 1D quadratic Klein-Gordon equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918397136076800 |
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| author | Bizoń, Piotr Romańczukiewicz, Tomasz |
| author_facet | Bizoń, Piotr Romańczukiewicz, Tomasz |
| contents | We study long-time dynamics of small even perturbations of the soliton in 1D quadratic Klein-Gordon equation. The soliton possesses both an internal mode and the unstable mode. On a codimension-one manifold of fine-tuned initial data the instability is suppressed and the internal mode decays slowly by transferring energy into the continuum. We show that this decay and the associated nonlinear frequency shift are accurately captured by a cubic resonant approximation, with the damping rate determined by a Fermi golde rule-type coefficient. This provides a quantitative description of irreversible energy transfer from the internal mode to dispersive radiation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18605 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Radiation damping of the soliton internal mode in 1D quadratic Klein-Gordon equation Bizoń, Piotr Romańczukiewicz, Tomasz Mathematical Physics Analysis of PDEs We study long-time dynamics of small even perturbations of the soliton in 1D quadratic Klein-Gordon equation. The soliton possesses both an internal mode and the unstable mode. On a codimension-one manifold of fine-tuned initial data the instability is suppressed and the internal mode decays slowly by transferring energy into the continuum. We show that this decay and the associated nonlinear frequency shift are accurately captured by a cubic resonant approximation, with the damping rate determined by a Fermi golde rule-type coefficient. This provides a quantitative description of irreversible energy transfer from the internal mode to dispersive radiation. |
| title | Radiation damping of the soliton internal mode in 1D quadratic Klein-Gordon equation |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2603.18605 |