Periodic nonlinear Schrödinger equation with application to photonic crystals. (English) Zbl 1225.35222
Summary: We present some results on existence of nontrivial solutions of periodic stationary nonlinear Schrödinger equations. We also sketch an application to nonlinear optics and discuss some open problems.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 58E50 | Applications of variational problems in infinite-dimensional spaces to the sciences |
| 78M30 | Variational methods applied to problems in optics and electromagnetic theory |
