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Symmetry 2019, 11(2), 161; https://doi.org/10.3390/sym11020161

A Note on Sign-Changing Solutions to the NLS on the Double-Bridge Graph

Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R. Cozzi 55, 20126 Milano, Italy
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Received: 15 January 2019 / Accepted: 28 January 2019 / Published: 1 February 2019
(This article belongs to the Special Issue Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks)
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Abstract

We study standing waves of the NLS equation posed on the double-bridge graph: two semi-infinite half-lines attached at a circle. At the two vertices, Kirchhoff boundary conditions are imposed. We pursue a recent study concerning solutions nonzero on the half-lines and periodic on the circle, by proving some existing results of sign-changing solutions non-periodic on the circle. View Full-Text
Keywords: quantum graphs; non-linear Schrödinger equation; standing waves quantum graphs; non-linear Schrödinger equation; standing waves
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Noja, D.; Rolando, S.; Secchi, S. A Note on Sign-Changing Solutions to the NLS on the Double-Bridge Graph. Symmetry 2019, 11, 161.

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