Singularly perturbed vector and scalar nonlinear Schrodinger equations with persistent homoclinic orbits

摘要

Singularly perturbed vector nonlinear Schrodinger equations (PVNLS) are investigated. Emphasis is placed upon the relation with their restriction: the singularly perturbed scalar nonlinear Schrodinger equation (PNLS) studied in [1]. It turns out that the persistent homoclinic orbit for the PNLS [1] is the only one for the PVNLS, asymptotic to the same saddle. [References: 17]