4 papers
Dispersion for the Schr{ö}dinger equation on the line with short-range array of delta potentials
Romain Duboscq, Élio 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 o…
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…
Analysis of quasi-periodic waves of cubic nonlinear Schr{ö}dinger equations
Perla Kfoury, Stefan Le Coz, Tai-Peng Tsai
We study the quasi-periodic standing wave solutions of the focusing and defocusing cubic nonlinear Schr{ö}dinger equations in dimension one. In the defocusing case, we establish a…
Stability of the multi-solitons of the modified Korteweg-de Vries equation
Stefan Le Coz, Zhong Wang
We establish the nonlinear stability of -soliton solutions of the modified Korteweg-de Vries (mKdV) equation. The -soliton solutions are global solutions of mKdV behaving at…