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Nonlinear Schrödinger equation on graphs: recent results and open problems
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Nonlinear Schrödinger equation on graphs: recent results and open problems
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Paper
Nonlinear Schrödinger equation on graphs: recent results and open problems
2013
Overview
In the present paper an introduction to the new subject of nonlinear dispersive hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of nonlinear Schr\"odinger equation. Special consideration is given to existence and behaviour of solitary solutions. Two subjects are discussed in some detail concerning NLS equation on a star graph: the standing waves of NLS equation on a graph with a \\(\\delta\\) interaction at the vertex; the scattering of fast solitons through an Y-junction in the cubic case. The emphasis is on description of concepts and results and on physical context, without reporting detailed proofs; some perspectives and more ambitious open problems are discussed.
Publisher
Cornell University Library, arXiv.org
Subject
