Construction of excited multi-solitons for the 5D energy-critical wave\n equation

2020/05/23 by Xu Yuan, Yuan, Xu · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2005.11496

openalex publication_date 2020/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the 5D energy-critical wave equation, we construct excited N-solitons\nwith collinear speeds, i.e. solutions u of the equation such that\n n
lim_t
to+
infty
bigg
|
nabla_t,xu(t)-
nabla_t,x
bigg(
sum_n=1^NQ_n(t)
bigg)
bigg
|_L²=0,\n where for n=1,\…,N, Q_n(t,x) is the Lorentz transform\nof a non-degenerate and sufficiently decaying excited state, each with\ndifferent but collinear speeds. The existence proof follows the ideas of\nMartel-Merle and C ^ote-Martel developed for the energy-critical wave and\nnonlinear Klein-Gordon equations. In particular, we rely on an energy method\nand on a general coercivity property for the linearized operator.\n

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• Existence of multi-solitons with any parameters for the 5D energy critical wave equation

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