Long-time asymptotics of 3-solitary waves for the damped nonlinear Klein-Gordon equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910006952067072 |
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| author | Ishizuka, Kenjiro |
| author_facet | Ishizuka, Kenjiro |
| contents | We consider the damped nonlinear Klein-Gordon equation: \begin{align*} \partial_{t}^2u-Δu+2α\partial_{t}u+u-|u|^{p-1}u=0, \ & (t,x) \in \mathbb{R} \times \mathbb{R}^d, \end{align*} where $α>0$, $1\leq d\leq 5$ and energy sub-critical exponents $p>2$. In this paper, we prove that 3-solitary waves behave as if the three solitons are on a line. Furthermore, the solitary waves have alternative signs and their distances are of order $\log{t}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_14889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-time asymptotics of 3-solitary waves for the damped nonlinear Klein-Gordon equation Ishizuka, Kenjiro Analysis of PDEs We consider the damped nonlinear Klein-Gordon equation: \begin{align*} \partial_{t}^2u-Δu+2α\partial_{t}u+u-|u|^{p-1}u=0, \ & (t,x) \in \mathbb{R} \times \mathbb{R}^d, \end{align*} where $α>0$, $1\leq d\leq 5$ and energy sub-critical exponents $p>2$. In this paper, we prove that 3-solitary waves behave as if the three solitons are on a line. Furthermore, the solitary waves have alternative signs and their distances are of order $\log{t}$. |
| title | Long-time asymptotics of 3-solitary waves for the damped nonlinear Klein-Gordon equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.14889 |