Аннотация
Abstract We deal with the construction of some special solutions for a two-component nonlinear Schrödinger system. More precisely, let $$R_1$$ R 1 and $$R_2$$ R 2 be two traveling waves of a scalar Schrödinger equation; our goal is to construct a solution of the system which behave at infinity like the pair $$(R_1,R_2)$$ ( R 1 , R 2 ) . Initially, we prove the existence of such solutions in dimensions $$1\le d\le 3$$ 1 ≤ d ≤ 3 with the assumption of relative high speeds between the solitary waves. We then finish our results by studying the one-dimensional case without the assumption of relative high speeds. The main tools used to establish our results combine several techniques including energy estimates, bootstrap, modulation and localization arguments.