Singularly perturbed vector and scalar nonlinear Schrödinger equations with persistent homoclinic orbits. (English) Zbl 1152.35496
Summary: Singularly perturbed vector nonlinear Schrödinger equations (PVNLS) are investigated. Emphasis is placed upon the relation with their restriction: The singularly perturbed scalar nonlinear Schrödinger 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.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B25 | Singular perturbations in context of PDEs |
| 37L99 | Infinite-dimensional dissipative dynamical systems |
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