Long-time asymptotics of (1,3)-sign solitary waves for the damped nonlinear Klein-Gordon equation
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910038640033792 |
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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 $α>0$, $2\leq d\leq 5$ and energy sub-critical exponents $p>2$. In this paper, we prove that any solution which is asymptotic to a superposition of four solitons with exactly one soliton of opposite sign evolves so that the three like-signed solitons spread out in an equilateral-triangle configuration centered at the oppositely signed soliton. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01205 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-time asymptotics of (1,3)-sign 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 $α>0$, $2\leq d\leq 5$ and energy sub-critical exponents $p>2$. In this paper, we prove that any solution which is asymptotic to a superposition of four solitons with exactly one soliton of opposite sign evolves so that the three like-signed solitons spread out in an equilateral-triangle configuration centered at the oppositely signed soliton. |
| title | Long-time asymptotics of (1,3)-sign solitary waves for the damped nonlinear Klein-Gordon equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.01205 |