In this 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 the nonlinear Schrödinger (NLS) equation. Special consideration is given to the existence and behaviour of solitary solutions. Two subjects are discussed in some detail concerning the NLS equation on a star graph: the standing waves of the NLS equation on a graph with a ? interaction at the vertex, and the scattering of fast solitons through a Y-junction in the cubic case. The emphasis is on a description of concepts and results and on physical context, without reporting detailed proofs; some perspectives and more ambitious open problems are discussed

Noja, D. (2013). Nonlinear Schrödinger equation on graphs: recent results and open problems. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 372(2007) [10.1098/rsta.2013.0002].

Nonlinear Schrödinger equation on graphs: recent results and open problems

NOJA, DIEGO DAVIDE
2013

Abstract

In this 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 the nonlinear Schrödinger (NLS) equation. Special consideration is given to the existence and behaviour of solitary solutions. Two subjects are discussed in some detail concerning the NLS equation on a star graph: the standing waves of the NLS equation on a graph with a ? interaction at the vertex, and the scattering of fast solitons through a Y-junction in the cubic case. The emphasis is on a description of concepts and results and on physical context, without reporting detailed proofs; some perspectives and more ambitious open problems are discussed
Articolo in rivista - Articolo scientifico
Nonlinear Schrödinger equation; Solitons; Stability
English
2013
372
2007
20130002
reserved
Noja, D. (2013). Nonlinear Schrödinger equation on graphs: recent results and open problems. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 372(2007) [10.1098/rsta.2013.0002].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/49536
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