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We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG)in $\mathbb{R}^{1+d}$, $d\ge1$, which behave as a soliton or a sum of solitonsin large time. In the spirit of other articles focusing on the supercriticalgeneralized Korteweg-de Vries equations and on the nonlinear Schr{\"o}dingerequations, we obtain an $N$-parameter family of solutions of (NLKG) whichconverges exponentially fast to a sum of given (unstable) solitons. For $N =1$, this family completely describes the set of solutions converging to thesoliton considered; for $N\ge 2$, we prove uniqueness in a class with explicitalgebraic rate of convergence.

On existence and uniqueness of asymptotic $N$-soliton-like solutions of the nonlinear klein-gordon equation