7 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…
Ground States for the Nonlinear Schr{ö}dinger Equation on Open Books and Dimensional Reduction to Metric Graphs
Stefan Le Coz, Boris Shakarov
In this work, we study the dimensional reduction of stationary states in the shrinking limit for a broad class of two-dimensional domains, called open books, to their counterparts…
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…
Traveling waves in periodic metric graphs via spatial dynamics
Stefan Le Coz, Dmitry E. Pelinovsky, Guido Schneider
The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{ö}dinger (NLS) equation on peri…
Ground states on a fractured strip and one dimensional reduction
Stefan Le Coz, Boris Shakarov
We consider the nonlinear Schr\''odinger equation on a strip with Neumann boundary conditions and a delta condition on the -axis. First, we show the existence of ground states a…
A minimal mass blow-up solution on a nonlinear quantum star graph
François Genoud, Stefan Le Coz, Julien Royer
We construct a finite-time blow-up solution to the mass-critical focusing nonlinear Schrödinger equation on a metric star graph with an arbitrary number of edges. We show that all…