Singularly Perturbed Vector and Scalar Nonlinear Schroedinger Equations   with Persistent Homoclinic Orbits
  Singularly perturbed vector nonlinear Schroedinger equations (PVNLS) are investigated. Emphasis is placed upon the relation with their restriction: The singularly perturbed scalar nonlinear Schroedinger equation (PNLS) studied earlier by Li. It turns out that the persistent homoclinic orbit for the PNLS is the only one for the PVNLS, asymptotic to the same saddle. 
Yanguang Charles Li