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In this paper, we construct $K$-solitons of the focusing energy-critical nonlinear wave equation in five-dimensional space, i.e. solutions $u$ of the equation such that begin{equation*} | abla_{t,x}u(t)- abla_{t,x}big(sum_{k=1}^{K}W_{k}(t)big)|_{L^{2}}to 0quad mathrm{as} tto infty, end{equation*} where for any $kin {1,dots,K}$, $W_{k}$ is Lorentz transform of the explicit standing soliton $W(x)=(1+|x|^{2}/15)^{-3/2}$, with any speed $boldsymbol{ell}_{k}in mathbb{R}^{5}$ ,$|boldsymbol{ell}_{k}|<1$ ($boldsymbol{ell}_{k} e boldsymbol{ell}_{k}$ for $k e k$) satisfying an explicit smallness condition.
For the 5D energy-critical wave equation, we construct excited $N$-solitons with collinear speeds, i.e. solutions $u$ of the equation such that begin{equation*} lim_{tto+infty}bigg| abla_{t,x}u(t)- abla_{t,x}bigg(sum_{n=1}^{N}Q_{n}(t)bigg)bigg|_{
Consider the focusing 4D cubic wave equation [ partial_{tt}u-Delta u-u^{3}=0,quad mbox{on} (t,x)in [0,infty)times mathbb{R}^{4}.] The main result states the existence in energy space $dot{H}^{1}times L^{2}$ of multi-solitary waves where each travelin
Consider a finite energy radial solution to the focusing energy critical semilinear wave equation in 1+4 dimensions. Assume that this solution exhibits type-II behavior, by which we mean that the critical Sobolev norm of the evolution stays bounded o
We consider the energy-critical non-linear focusing wave equation in dimension N=3,4,5. An explicit stationnary solution, $W$, of this equation is known. The energy E(W,0) has been shown by C. Kenig and F. Merle to be a threshold for the dynamical be
Consider the energy-critical focusing wave equation in space dimension $Ngeq 3$. The equation has a nonzero radial stationary solution $W$, which is unique up to scaling and sign change. It is conjectured (soliton resolution) that any radial, bounded