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Classification of multi-solitons in one sense of time for the 5D energy-critical wave equation
Abstract
We classify the multi-solitons, in the positive sense of time, of the focusing energy-critical wave equation in space dimension $5$, more precisely the solutions u(t,x) of the equation ∂t2 u − Δu − |u|4/3 u = 0, (t,x)∈ [T0,∞)× ℝ5, which satisfy the estimate |∇t,x (u(t) − ∑k Wk(t) ) |L2 ≲ t−1/2+ for all $t≫ 1$. Here, {Wk}k is any given finite family of traveling waves, based on the explicit ground state solution W(x) = (1+ |x|2/15)−3/2 with collinear two-by-two different velocities.
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BibTeX
@misc{martel2026classification,
title = {{Classification of multi-solitons in one sense of time for the 5D energy-critical wave equation}},
author = {Yvan Martel and Frank Merle},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09967},
eprint = {2609.09967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09967},
}
RIS
TY - UNPB
TI - Classification of multi-solitons in one sense of time for the 5D energy-critical wave equation
AU - Yvan Martel
AU - Frank Merle
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09967
UR - https://arxiv.org/abs/2609.09967
AB - We classify the multi-solitons, in the positive sense of time, of the focusing energy-critical wave equation in space dimension $5$, more precisely the solutions u(t,x) of the equation ∂_t^2 u − Δu − |u|^4/3 u = 0, (t,x)∈ [T_0,∞)× ℝ^5, which satisfy the estimate |∇_t,x (u(t) − ∑_k W_k(t) ) |_L^2 ≲ t^−1/2^+ for all $t≫ 1$. Here, {W_k}_k is any given finite family of traveling waves, based on the explicit ground state solution W(x) = (1+ |x|^2/15)^−3/2 with collinear two-by-two different velocities.
ER -