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Variational properties and orbital stability of standing waves for NLS equation on a star graph
We study standing waves for a model of nonlinear Schr\"odinger equation on a graph. The graph is obtained joining $N$ halflines at a vertex, i.e. it is a star graph. At the vertex an interactionExpand
Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy
On a star graph made of $N \geq 3$ halflines (edges) we consider a Schrodinger equation with a subcritical power-type nonlinearity and an attractive delta interaction located at the vertex. FromExpand
Stability and Symmetry-Breaking Bifurcation for the Ground States of a NLS with a δ′ Interaction
We determine and study the ground states of a focusing Schrödinger equation in dimension one with a power nonlinearity |ψ|2μψ and a strong inhomogeneity represented by a singular point perturbation,Expand
Nonlinear Schrödinger equation on graphs: recent results and open problems
  • D. Noja
  • Mathematics, Physics
  • Philosophical Transactions of the Royal Society A…
  • 3 April 2013
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 theExpand
We define the Schrodinger equation with focusing, cubic nonlinearity on one-vertex graphs. We prove global well-posedness in the energy domain and conservation laws for some self-adjoint boundaryExpand
Existence of Dynamics for a 1 − d NLS equation perturbed with a generalized point defect
In the present paper we study the well-posedness for the one-dimensional cubic NLS perturbed by a generic point interaction. Point interactions are described as the 4-parameter family of self-adjointExpand
Constrained energy minimization and ground states for NLS with point defects
We investigate the ground states of the one-dimensional nonlinear Schr\"odinger equation with a defect located at a fixed point. The nonlinearity is focusing and consists of a subcritical power. TheExpand
Bifurcations and stability of standing waves in the nonlinear Schr\"odinger equation on the tadpole graph
We develop a detailed rigorous analysis of edge bifurcations of standing waves in the nonlinear Schr\"odinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to theExpand
Constrained energy minimization and orbital stability for the NLS equation on a star graph
Abstract On a star graph G , we consider a nonlinear Schrodinger equation with focusing nonlinearity of power type and an attractive Dirac's delta potential located at the vertex. The equation can beExpand
On the structure of critical energy levels for the cubic focusing NLS on star graphs
We provide information on a non-trivial structure of phase space of the cubic nonlinear Schrodinger (NLS) on a three-edge star graph. We prove that, in contrast to the case of the standard NLS on theExpand