Surgery principles for the spectral analysis of quantum graphs
We present a systematic collection of spectral surgery principles for the Laplacian on a
compact metric graph with any of the usual vertex conditions (natural, Dirichlet, or $\delta …
compact metric graph with any of the usual vertex conditions (natural, Dirichlet, or $\delta …
Nonlinearity+ networks: A 2020 vision
MA Porter - Emerging frontiers in nonlinear science, 2020 - Springer
I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few
methods and ideas, including several of personal interest, that I anticipate to be especially …
methods and ideas, including several of personal interest, that I anticipate to be especially …
Negative Energy Ground States for the L 2-Critical NLSE on Metric Graphs
We investigate the existence of ground states with prescribed mass for the focusing
nonlinear Schrödinger equation with L 2-critical power nonlinearity on noncompact quantum …
nonlinear Schrödinger equation with L 2-critical power nonlinearity on noncompact quantum …
Standing waves on quantum graphs
We review evolutionary models on quantum graphs expressed by linear and nonlinear
partial differential equations. Existence and stability of the standing waves trapped on …
partial differential equations. Existence and stability of the standing waves trapped on …
Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
We consider a nonlinear Schrödinger equation (NLS) posed on a graph (or network)
composed of a generic compact part to which a finite number of half-lines are attached. We …
composed of a generic compact part to which a finite number of half-lines are attached. We …
Standing waves of the quintic NLS equation on the tadpole graph
D Noja, DE Pelinovsky - Calculus of Variations and Partial Differential …, 2020 - Springer
The tadpole graph consists of a circle and a half-line attached at a vertex. We analyze
standing waves of the nonlinear Schrödinger equation with quintic power nonlinearity …
standing waves of the nonlinear Schrödinger equation with quintic power nonlinearity …
An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity
We present a brief overview of the existence/nonexistence of standing waves for the
NonLinear Schrödinger and the NonLinear Dirac Equations (NLSE/NLDE) on metric graphs …
NonLinear Schrödinger and the NonLinear Dirac Equations (NLSE/NLDE) on metric graphs …
Bifurcations of standing localized waves on periodic graphs
D Pelinovsky, G Schneider - Annales Henri Poincaré, 2017 - Springer
The nonlinear Schrödinger (NLS) equation is considered on a periodic graph subject to the
Kirchhoff boundary conditions. Bifurcations of standing localized waves for frequencies lying …
Kirchhoff boundary conditions. Bifurcations of standing localized waves for frequencies lying …
Nonlinear Dirac equation on graphs with localized nonlinearities: bound states and nonrelativistic limit
In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs
with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices …
with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices …
Numerical simulations on nonlinear quantum graphs with the GraFiDi library
Nonlinear quantum graphs are metric graphs equipped with a nonlinear Schrödinger
equation. Whereas in the last ten years they have known considerable developments on the …
equation. Whereas in the last ten years they have known considerable developments on the …