Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Infinitely many radial solutions of a variational problem related to dispersion-managed optical fibers

Author(s): Markus Kunze
Journal: Proc. Amer. Math. Soc. 131 (2003), 2181-2188.
MSC (1991): Primary 35A15, 35Q55; Secondary 78A60
Posted: November 13, 2002
MathSciNet review: 1963766
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Abstract: We consider a non-local variational problem whose critical points are related to bound states in certain optical fibers. The functional is given by $\varphi(u)=\frac{1}{2}\vert u\vert^2_{H^1}-\int_0^1\int_{\mathbb R^2}\vert e^{it\Delta}u\vert^4\,dxdt$ , and relying on the regularizing properties of the solution $e^{it\Delta}$ to the free Schrödinger equation, it will be shown that $\varphi$ has infinitely many critical points.

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