4 papers
Dispersion for the Schr{ö}dinger equation on the line with short-range array of delta potentials
Romain Duboscq, Ãlio Durand-Simonnet, Stefan Le Coz
We study dispersive properties of the one-dimensional Schr{ö}dinger equation with a short-range array of delta interactions. More precisely, we consider the self-adjoint operator…
On the defocusing stationary nonlinear Schrödinger equation on metric graphs
Ãlio Durand-Simonnet, Damien Galant, Boris Shakarov
We study the defocusing nonlinear Schrödinger equation on noncompact metric graphs under general self-adjoint vertex conditions ensuring the existence of a negative eigenvalue of…
Ground States for the Defocusing Nonlinear Schrödinger Equation on Non-Compact Metric Graphs
Ãlio Durand-Simonnet, Boris Shakarov
We investigate the existence and stability of ground states for the defocusing nonlinear Schrödinger equation on non-compact metric graphs. We establish a sharp criterion for the…
Ground States of the Nonlinear Schr{ö}dinger Equation on the Tadpole Graph with a Repulsive Delta Vertex Condition
Romain Duboscq, Ãlio Durand-Simonnet, Stefan Le Coz
We consider the stationary nonlinear Schr{ö}dinger equation set on a tadpole graph with a repulsive delta vertex condition between the loop and the tail of the tadpole. We establi…