Infinitely many radial solutions of a variational problem related to dispersion-managed optical fibers
Infinitely many radial solutions of a variational problem related to dispersion-managed optical fibers
We consider a non-local variational problem whose critical points are related to bound states in certain optical fibers. The functional is given by $\varphi (u)=\frac {1}{2}|u|^2_{H^1}-\int _0^1\int _{\mathbb {R}^2}|e^{it\Delta }u|^4 dxdt$, and relying on the regularizing properties of the solution $e^{it\Delta }$ to the free Schrödinger equation, it will be …