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We study pointwise spatial decay of multi-solitons of the generalizedKorteweg-de Vries equations. We obtain that, uniformly in time, these solutionsand their derivatives decay exponentially in space on the left of and in thesolitons region, and prove rapid decay on the right of the solitons. We alsoprove the corresponding result for multi-solitons of the nonlinearSchr{\"o}dinger equations, that is, exponential decay in the solitons regionand rapid decay outside.

Spatial decay of multi-solitons of the generalized Korteweg-de Vries and nonlinear Schr{\"o}dinger equations