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- W2952279905 abstract "We consider a generalized nonlinear Schrodinger equation (NLS) with a power nonlinearity |psi|^2mupsi, of focusing type, describing propagation on the ramified structure given by N edges connected at a vertex (a star graph). To model the interaction at the junction, it is there imposed a boundary condition analogous to the delta potential of strength alpha on the line, including as a special case (alpha=0) the free propagation. We show that nonlinear stationary states describing solitons sitting at the vertex exist both for attractive (alpha 0, a potential barrier) interaction. In the case of sufficiently strong attractive interaction at the vertex and power nonlinearity mu<2, including the standard cubic case, we characterize the ground state as minimizer of a constrained action and we discuss its orbital stability. Finally we show that in the free case, for even N only, the stationary states can be used to construct traveling waves on the graph." @default.
- W2952279905 created "2019-06-27" @default.
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- W2952279905 date "2011-04-19" @default.
- W2952279905 modified "2023-09-23" @default.
- W2952279905 title "Stationary States of NLS on Star Graphs" @default.
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