8 papers
Transverse Instability and Bifurcation Analysis of the line soliton for the NLS equation on a Fractured Strip
Hiroaki Kikuchi, Boris Shakarov, Kenta Tomioka
We consider the nonlinear Schrödinger equation on a two-dimensional strip with an attractive interaction and power nonlinearity. We investigate the transverse stability and bif…
Scattering for Defocusing NLS with Inhomogeneous Nonlinear Damping and Nonlinear Trapping Potential
David Lafontaine, Boris Shakarov
We investigate an energy-subcritical defocusing nonlinear Schrödinger equation in subject to a lower order nonlinear trapping potential and a spatially dependent non…
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 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 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…
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 ad…