PreprintCC BY 4.0arXiv
Classification and long-time asymptotics of (2,2)-sign solitons for the damped nonlinear Klein-Gordon equation
Abstract
We consider the damped nonlinear Klein-Gordon equation ∂t2u−Δu+2α∂tu+u−|u|p−1u=0 on ℝd, where α>0, 2≤ d≤5, and p>2 is in the energy-subcritical range. We classify global solutions that converge to a superposition of two positive and two negative translates of the ground state, without imposing any symmetry, coplanarity, or a priori geometric condition on their centers. We prove that every such four-soliton configuration is asymptotically either an alternating collinear configuration or an expanding rhombus with alternating signs. We further determine the precise long-time asymptotics of all four centers.
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BibTeX
@misc{kenjiro2026classification,
title = {{Classification and long-time asymptotics of $(2,2)$-sign solitons for the damped nonlinear Klein-Gordon equation}},
author = {Ishizuka Kenjiro},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13207},
eprint = {2609.13207},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13207},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classification and long-time asymptotics of (2,2)-sign solitons for the damped nonlinear Klein-Gordon equation
AU - Ishizuka Kenjiro
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.13207
UR - https://arxiv.org/abs/2609.13207
AB - We consider the damped nonlinear Klein-Gordon equation ∂_t^2u−Δu+2α∂_tu+u−|u|^p−1u=0 on ℝ^d, where α>0, 2≤ d≤5, and p>2 is in the energy-subcritical range. We classify global solutions that converge to a superposition of two positive and two negative translates of the ground state, without imposing any symmetry, coplanarity, or a priori geometric condition on their centers. We prove that every such four-soliton configuration is asymptotically either an alternating collinear configuration or an expanding rhombus with alternating signs. We further determine the precise long-time asymptotics of all four centers.
ER -