Atanas G. Stefanov

Professor · Department of Mathematics · University of Alabama at Birmingham

I am a Professor in the Department of Mathematics at the University of Alabama at Birmingham (UAB). My research is in the analysis of partial differential equations, in particular soliton and near-soliton dynamics, local and global behavior of dispersive PDE, and asymptotics for dissipative PDE.

Before joining UAB in 2021, I was a Professor in the Department of Mathematics at the University of Kansas. I received my Ph.D. in Mathematics from the University of Missouri in 1999.

Email: stefanov@uab.edu

Phone: (205) 934-8551

Office: University Hall, Room 4005

Address: 1402 10th Avenue S., Birmingham, AL 35294-1241

Appointments

Research

My interests lie in the analysis of partial differential equations:

• Soliton dynamics — linear and nonlinear stability of solitary waves in dispersive models, asymptotic stability; solitary waves in spatially discrete systems.
• Dispersive PDE — local and global behavior of nonlinear Schrödinger, wave, Klein–Gordon, Dirac, KdV, Ostrovsky and Whitham models.
• Dissipative PDE — well-posedness, regularity and sharp asymptotics for fluid models such as the Boussinesq system and the quasi-geostrophic equation.

My research is currently supported by NSF grant DMS-2605398, Beyond Scalar Models: Variational Methods, Stability and Dynamics for Infinite Dimensional Dynamical Systems (2026–2029).

A complete list of publications is in my CV.

Recent publications

1. A. G. Stefanov, Asymptotic stability for monotone traveling kinks of the dissipative Boussinesq problem. Submitted. arXiv
2. A. G. Stefanov, J. Wu, X. Xu, Z. Ye, Global regularity of the 2D fractional Boussinesq equations with subcritical dissipation. Submitted. arXiv
3. M. Stanislavova, A. G. Stefanov, J. Cuevas-Maraver, P. G. Kevrekidis, On a Klein–Gordon reduction for oscillons. J. Nonlinear Waves 2 (2026), e11. Open accessarXiv
4. A. G. Stefanov, P. G. Kevrekidis, Kinks of fractional φ⁴ models: existence, uniqueness, stability, monotonicity and sharp asymptotics. Nonlinearity 39 (2026), no. 5, 055007. Open accessarXiv
5. V. Iyer, R. Parker, A. G. Stefanov, Existence and stability for traveling waves of fourth order semilinear wave and Schrödinger equations. Stud. Appl. Math. 156 (2026), no. 4, Paper No. e70214. Open accessarXiv
6. M. Stanislavova, A. G. Stefanov, Asymptotic attraction with algebraic rates toward fronts of dispersive-diffusive Burgers equations. J. Nonlinear Waves 1 (2025), 1–16. Open accessarXiv
7. O. Christov, S. Hakkaev, S. Oh, A. G. Stefanov, Dynamics of the Drinfeld–Sokolov–Wilson system: well-posedness and (in)stability of the traveling waves. J. Differential Equations 439 (2025), 113410. arXiv
8. S. Hakkaev, M. Stanislavova, A. G. Stefanov, Existence and stability for the travelling waves of the Benjamin equation. Nonlinearity 38 (2025), 025020. Open accessarXiv
9. S. Hakkaev, A. G. Stefanov, On the stability of the dnoidal waves for the Schrödinger–KdV system. Proc. Amer. Math. Soc. 153 (2025), 715–725. arXiv
10. V. Iyer, A. G. Stefanov, Solitary waves for power degenerate NLS — existence and stability. Calc. Var. Partial Differential Equations 64 (2025), no. 1, Paper No. 19. Open accessarXiv

Selected publications

1. S. Hakkaev, M. Stanislavova, A. G. Stefanov, Existence and stability for the travelling waves of the Benjamin equation. Nonlinearity 38 (2025), 025020. Open access
2. A. G. Stefanov, R. M. Ross, P. G. Kevrekidis, Ground states in spatially discrete non-linear Schrödinger lattices. Nonlinearity 36 (2023), no. 8, 4053–4085. PDF
3. S. Hakkaev, M. Stanislavova, A. G. Stefanov, On the stability of periodic waves for the cubic derivative NLS and the quintic NLS. J. Nonlinear Sci. 31 (2021), no. 54. arXiv
4. A. G. Stefanov, On the normalized ground states of second order PDE's with mixed power non-linearities. Comm. Math. Phys. 369 (2019), no. 3, 929–971.
5. A. Comech, T. V. Phan, A. G. Stefanov, Asymptotic stability of solitary waves in generalized Gross–Neveu model. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 1, 157–196.
6. M. Stanislavova, A. G. Stefanov, On the spectral problem Lu = λu′ and applications. Comm. Math. Phys. 343 (2016), no. 2, 361–391.
7. A. G. Stefanov, P. G. Kevrekidis, On the existence of solitary traveling waves for generalized Hertzian chains. J. Nonlinear Sci. 22 (2012), no. 3, 327–349.
8. A. G. Stefanov, P. G. Kevrekidis, Asymptotic behavior of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations. Nonlinearity 18 (2005), 1841–1857.
9. A. Nahmod, A. G. Stefanov, K. Uhlenbeck, On the well-posedness of the wave map problem in high dimensions. Comm. Anal. Geom. 11 (2003), 49–83.
10. A. Nahmod, A. G. Stefanov, K. Uhlenbeck, On Schrödinger maps. Comm. Pure Appl. Math. 56 (2003), 114–151; Erratum: Comm. Pure Appl. Math. 57 (2004), 833–839.

NSF Grants

Current

Past

Teaching

Graduate courses

Mathematical Analysis I, II · Real Analysis / Measure Theory · Complex Analysis · Functional Analysis I, II · Fourier Analysis and PDE · Advanced PDE

Undergraduate courses

Calculus I, II, III · Linear Algebra · Elementary ODE · Calculus of Variations · Applied PDE

Teaching awards

• Max Wells Teaching Award, University of Kansas, 2019
• G. Baley Price Teaching Award (KU Mathematics Graduate Student Association), 2018

Ph.D. Students

Current students

• Malihe Farziharomi, University of Alabama at Birmingham
• Muhammad Saqib, University of Alabama at Birmingham

Former students

Curriculum Vitae

My full CV, including the complete publication list, grants and invited talks.