3 citations · 8 across the 13 of their papers we have counts for
14 papers
Asymptotic stability and sharp decay near homogeneous solutions of a nonlinearly damped Schrödinger equation on the torus
Boris Shakarov
We study the one-dimensional periodic nonlinear Schrödinger equation with a power-type nonlinear damping, both in the focusing and the defocusing regime. For a sufficiently small d…
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 nonl…
On the defocusing stationary nonlinear Schrödinger equation on metric graphs
Élio 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 t…
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…
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…
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…
Global solutions and Asymptotic Behavior to a Norm-preserving Non-local Parabolic Flow
Boris Shakarov
We consider a nonlinear parabolic model that forces solutions to stay on a -sphere through a nonlocal term in the equation. We study the local and global well-posedness on a b…
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…
On the formation of singularities for the slightly supercritical NLS equation with nonlinear damping
Paolo Antonelli, Boris Shakarov
We consider the focusing, mass-supercritical NLS equation augmented with a nonlinear damping term. We provide sufficient conditions on the nonlinearity exponents and damping coeffi…
Existence and Large Time Behavior for a Dissipative Variant of the Rotational NLS Equation
Paolo Antonelli, Boris Shakarov
We study a dissipative variant of the Gross-Pitaevskii equation with rotation. The model contains a nonlocal, nonlinear term that forces the conservation of -norm of solutions…
Stability of Cnoidal Waves for the Damped Nonlinear Schrödinger Equation
Paolo Antonelli, Boris Shakarov
We consider the cubic nonlinear Schrödinger (NLS) equation with a linear damping on the one dimensional torus and we investigate the stability of some solitary wave profiles within…
Existence and asymptotic behavior for -norm preserving nonlinear heat equations
Paolo Antonelli, Piermarco Cannarsa, Boris Shakarov
We consider a nonlinear parabolic equation with a nonlocal term, which preserves the -norm of the solution. We study the local and global well posedness on a bounded domain, a…
Global Large Data Solutions of 2D Dirac Equation with Hartree Type Interaction
Vladimir Georgiev, Boris Shakarov
Local and global well - posedness of the solution to the two space dimensional Dirac equation with Hartree type nonlinearity is established with the initial datum in the space $H^s…