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arXiv · 2503.14889

Long-time asymptotics of 3-solitary waves for the damped nonlinear Klein-Gordon equation

Kenjiro Ishizuka
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Abstract

We consider the damped nonlinear Klein-Gordon equation: \begin{align*} \partial_{t}^2u-\Delta u+2\alpha \partial_{t}u+u-|u|^{p-1}u=0, \ & (t,x) \in \mathbb{R} \times \mathbb{R}^d, \end{align*} where $\alpha>0$, $1\leq d\leq 5$ 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 $\log{t}$.

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Kenjiro Ishizuka. 2025-03-19. Long-time asymptotics of 3-solitary waves for the damped nonlinear Klein-Gordon equation. https://arxiv.org/abs/2503.14889

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