Abstract We deal with the construction of some special solutions for a two-component nonlinear Schrödinger system. More precisely, let R₁ R 1 and R₂ 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 (R₁, R₂) (R 1, R 2). Initially, we prove the existence of such solutions in dimensions 1 d 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.
Alvarez et al. (Mon,) studied this question.