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math.AP2025
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…
math.AP2025
Scattering for defocusing cubic NLS under locally damped strong trapping
David Lafontaine, Boris Shakarov
We are interested in the scattering problem for the cubic 3D nonlinear defocusing Schrödinger equation with variable coefficients. Previous scattering results for such problems add…
math.AP2025
Ground States for the Defocusing Nonlinear Schrödinger Equation on Non-Compact Metric Graphs
Élio 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 e…