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

Author:
Markus Kunze

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2181-2188

MSC (1991):
Primary 35A15, 35Q55; Secondary 78A60

DOI:
https://doi.org/10.1090/S0002-9939-02-06780-1

Published electronically:
November 13, 2002

MathSciNet review:
1963766

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 , and relying on the regularizing properties of the solution to the free Schrödinger equation, it will be shown that has infinitely many critical points.

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Additional Information

**Markus Kunze**

Affiliation:
FB 6 – Mathematik, Universität Essen, D-45117 Essen, Germany

Email:
mkunze@ing-math.uni-essen.de

DOI:
https://doi.org/10.1090/S0002-9939-02-06780-1

Keywords:
Nonlocal variational problem,
compactness by symmetry,
infinitely many solutions,
nonlinear optics,
dispersion managed solitons

Received by editor(s):
December 13, 2001

Received by editor(s) in revised form:
March 3, 2002

Published electronically:
November 13, 2002

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2002
American Mathematical Society