Research Activity

Preprints

Shakarov, B. (2026). Asymptotic stability and sharp decay near homogeneous solutions of a nonlinearly damped Schrödinger equation on the torus. arXiv:2610.16526.

Kikuchi, H., Shakarov, B., and Tomioka, K. (2026). Transverse Instability and Bifurcation Analysis of the Line Soliton for the NLS Equation on a Fractured Strip. arXiv:2608.09553.

Lafontaine, D., and Shakarov, B. (2026). Scattering for Defocusing NLS with Inhomogeneous Nonlinear Damping and Nonlinear Trapping Potential. arXiv:2603.11765.

Le Coz, S., and Shakarov, B. (2025). Ground States for the Nonlinear Schrödinger Equation on Open Books and Dimensional Reduction to Metric Graphs. HAL: hal-05425865.

Publications

Le Coz, S., and Shakarov, B. (2026). Ground states on a fractured strip and one-dimensional reduction. Z. Anal. Anwend. Journal article.

Durand-Simonnet, È., Galant, D., and Shakarov, B. (2026). On the defocusing stationary nonlinear Schrödinger equation on metric graphs. Journal of Differential Equations. DOI.

Durand-Simonnet, È., and Shakarov, B. (2026). Existence and stability of ground states for the defocusing nonlinear Schrödinger equation on Quantum Graphs. Commun. Pure Appl. Anal. DOI.

Lafontaine, D., and Shakarov, B. (2026). Scattering for defocusing cubic NLS under locally damped strong trapping. Annales Henri Lebesgue 9, 147–184. Journal article · DOI · arXiv:2502.06306.

Antonelli, P., and Shakarov, B. (2025). On the formation of singularity for the slightly supercritical NLS equation with nonlinear damping. J. Dyn. Diff. Equat. DOI.

Shakarov, B. (2025). Global Solutions and Asymptotic Behavior to a Norm-preserving Non-local Parabolic Flow. Boll. Unione Mat. Ital. 18, 1215–1234. DOI.

Antonelli, P., and Shakarov, B. (2024). Stability of cnoidal waves for the damped nonlinear Schrödinger equation. J. Hyperbolic Differ. Equ. 21(4), 1045–1086. DOI.

Antonelli, P., and Shakarov, B. (2024). Existence and large time behavior for a dissipative variant of the rotational NLS equation. Commun. Math. Sci. 22(6), 1601–1633. DOI.

Antonelli, P., Cannarsa, P., and Shakarov, B. (2024). Existence and asymptotic behavior for L²-norm preserving nonlinear heat equations. Calc. Var. 63, 108. DOI.

Georgiev, V., and Shakarov, B. (2022). Global large data solutions for 2D Dirac equation with Hartree-type interaction. Int. Math. Res. Notices 2022(17), 12803–12820. DOI.

Georgiev, V., and Shakarov, B. (2019). The boson star equation with Hartree-type nonlinearity: global existence in H¹ᐟ²(ℝ²). Pliska Studia Mathematica Bulgarica 30(1). Publication.