Positions

Selected Publications

Academic Article

Year Title Altmetric
2022 ON THE STABILITY OF THE COMPACTON WAVES FOR THE DEGENERATE KDV AND NLS MODELS.  Quarterly of Applied Mathematics.  80:507-528. 2022
2021 Smoothing and growth bound of periodic generalized Korteweg-De Vries equation.  Journal of Hyperbolic Differential Equations.  18:899-930. 2021
2021 On the Barashenkov-Bogdan-Zhanlav solitons and their stability.  Chaos, Solitons and Fractals.  152. 2021
2021 Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle.  Journal of Differential Equations.  297:25-46. 2021
2021 On the standing waves of the Schrödinger equation with concentrated nonlinearity 2021
2021 Stability of periodic waves for the fractional KdV and NLS equations 2021
2021 On the Stability of Periodic Waves for the Cubic Derivative NLS and the Quintic NLS 2021
2021 Ground states for the nonlinear Schrödinger equation under a general trapping potential 2021
2021 On the Forced Surface Quasi-Geostrophic Equation: Existence of Steady States and Sharp Relaxation Rates 2021
2020 Existence and stability of solitary waves for the inhomogeneous NLS.  Physica D: Nonlinear Phenomena.  414. 2020
2020 On the normalized ground states for the Kawahara equation and a fourth order NLS 2020
2020 On the ground states of the Ostrovskyi equation and their stability 2020
2020 Sharp relaxation rates for plane waves of general reaction-diffusion models.  Journal of Mathematical Physics.  61. 2020
2020 Small Amplitude Traveling Waves in the Full-Dispersion Whitham Equation 2020
2019 On the Sharp Time Decay Rates for the 2D Generalized Quasi-geostrophic Equation and the Boussinesq System 2019
2019 On the Normalized Ground States of Second Order PDE’s with Mixed Power Non-linearities.  Communications in Mathematical Physics.  369:929-971. 2019
2019 A global regularity result for the 2D Boussinesq equations with critical dissipation 2019
2019 On the generation of stable Kerr frequency combs in the Lugiato–Lefever model of periodic optical waveguides∗.  SIAM Journal on Applied Mathematics.  79:477-505. 2019
2018 Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguides.  Journal of Mathematical Physics.  59. 2018
2018 On the spectral stability of ground states of semi-linear Schrödinger and Klein-Gordon equations with fractional dispersion 2018
2018 On the classification of the spectrally stable standing waves of the Hartree problem.  Physica D: Nonlinear Phenomena.  370:29-39. 2018
2017 On the stability of standing waves for PT symmetric Schrödinger and Klein-Gordon equations in higher space dimensions.  Proceedings of the American Mathematical Society.  145:5273-5285. 2017
2017 Spectral Stability for Classical Periodic Waves of the Ostrovsky and Short Pulse Models 2017
2017 A global regularity result for the 2D Boussinesq equations with critical dissipation 2017
2017 Asymptotic stability of solitary waves in generalized Gross–Neveu model 2017
2017 On the global regularity of the 2D critical Boussinesq system with α > 2/3 2017
2017 Periodic traveling waves of the regularized short pulse and Ostrovsky equations: Existence and stability.  SIAM Journal on Mathematical Analysis.  49:674-698. 2017
2016 Traveling Waves for the Mass in Mass Model of Granular Chains.  Letters in Mathematical Physics.  106:1067-1088. 2016
2016 On the Spectral Problem Lu=λ′ and Applications.  Communications in Mathematical Physics.  343:361-391. 2016
2015 Traveling waves and their tails in locally resonant granular systems 2015
2014 On the Spectral Stability of Kinks in Some PT-Symmetric Variants of the Classical Klein-Gordon Field Theories 2014
2014 A Hamiltonian-Krein (Instability) index theory for solitary waves to KdV-Like eigenvalue problems 2014
2014 Linear stability analysis for periodic travelling waves of the Boussinesq equation and the Klein-Gordon-Zakharov system 2014
2013 Spectral stability for subsonic traveling pulses of the boussinesq "abc" system 2013
2013 Effects of parity-time symmetry in nonlinear Klein-Gordon models and their stationary kinks 2013
2013 Global Regularity for the Quadratic Klein-Gordon Equation in R1+2.  Communications in Partial Differential Equations.  38:1287-1312. 2013
2013 Optimal control for a mixed flow of hamiltonian and gradient type in space of probability measures.  Transactions of the American Mathematical Society.  365:3987-4039. 2013
2013 Improved local well-posedness for the periodic "good" Boussinesq equation.  Journal of Differential Equations.  254:4047-4065. 2013
2013 Orbital stability for periodic standing waves of the Klein-Gordon-Zakharov system and the beam equation 2013
2013 Traveling waves for monomer chains with precompression.  Nonlinearity.  26:539-564. 2013
2013 Spectral stability analysis for special solutions of second order in time PDEs: The higher dimensional case.  Physica D: Nonlinear Phenomena.  262:1-13. 2013
2012 Transverse instability for periodic waves of KP-I and schrödinger equations.  Indiana University Mathematics Journal.  61:461-492. 2012
2012 Preface: Recent progress on the long time behavior of coherent structures in discrete and continuous models 2012
2012 Linear stability analysis for travelling waves of second order in time PDE's.  Nonlinearity.  25:2625-2654. 2012
2012 Asymptotic stability of small gap solitons in nonlinear Dirac equations.  Journal of Mathematical Physics.  53. 2012
2012 On the existence of solitary traveling waves for generalized Hertzian chains 2012
2012 On quadratic Schrödinger equations in R1+1: A normal form approach 2012
2011 Erratum to: Asymptotic estimates and stability analysis of Kuramoto-Sivashinsky type models (J. Evol. Equ., 10.1007/s00028-011-0103-5) 2011
2011 Global regularity for the minimal surface equation in Minkowskian geometry.  Forum Mathematicum.  23:757-789. 2011
2011 Asymptotic estimates and stability analysis of Kuramoto-Sivashinsky type models 2011
2010 Well-posedness and small data scattering for the generalized Ostrovsky equation.  Journal of Differential Equations.  249:2600-2617. 2010
2010 Global regularity for Yang-Mills fields in R1+5.  Journal of Hyperbolic Differential Equations.  7:433-470. 2010
2010 On the Lipschitzness of the solution map for the 2 D Navier-Stokes system 2010
2010 Pseudodifferential operators with rough symbols 2010
2009 Asymptotic stability of small bound states in the discrete nonlinear schrodinger equation.  SIAM Journal on Mathematical Analysis.  41:2010-2030. 2009
2009 Decay and Strichartz estimates for DNLS 2009
2009 On precise center stable manifold theorems for certain reaction-diffusion and Klein-Gordon equations.  Physica D: Nonlinear Phenomena.  238:2298-2307. 2009
2008 On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension.  Journal of Mathematical Physics.  49. 2008
2008 Erratum to: "Dynamical barrier for the formation of solitary waves in discrete lattices" [Phys. Lett. A 372 (2008) 2247] (DOI:10.1016/j.physleta.2007.11.029) 2008
2008 Dynamical barrier for the formation of solitary waves in discrete lattices 2008
2007 Global well-posedness for the 2D quasi-geostrophic equation in a critical besov space.  Electronic Journal of Differential Equations.  2007:1-9. 2007
2007 On quadratic derivative Schrödinger equations in one space dimension.  Transactions of the American Mathematical Society.  359:3589-3607. 2007
2007 Strichartz estimates for the magnetic Schrödinger equation.  Advances in Mathematics.  210:246-303. 2007
2007 Attractors for the viscous Camassa-Holm equation 2007
2007 Smoothing - Strichartz estimates for the schrödinger equation with small magnetic potential 2007
2006 Nonlinearity management in higher dimensions 2006
2006 On some Schrödinger and wave equations with time dependent potentials.  Mathematische Annalen.  334:325-338. 2006
2005 Asymptotic smoothing and attractors for the generalized Benjamin-Bona-Mahony equation on R3.  Journal of Differential Equations.  219:451-483. 2005
2005 On global finite energy solutions of the Camassa-Holm equation 2005
2005 Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations.  Nonlinearity.  18:1841-1857. 2005
2004 Erratum: On Schrödinger maps.  Communications on Pure and Applied Mathematics.  57:833-839. 2004
2004 Erratum: On Schrödinger maps (Communications on Pure and Applied Mathematics (2003) 56, 1 (114-151)).  Communications on Pure and Applied Mathematics.  57:0833-0839. 2004
2004 Calderón-Zygmund operators on mixed Lebesgue spaces and applications to null forms 2004
2003 On Schrödinger Maps.  Communications on Pure and Applied Mathematics.  56:114-151. 2003
2003 On the well-posedness of the wave map problem in high dimensions 2003
2001 Strichartz estimates for the Schrödinger equation with radial data.  Proceedings of the American Mathematical Society.  129:1395-1401. 2001
2001 Weak type estimates for certain Calderón-Zygmund singular integral operators 2001
2000 Characterizations of H1 and applications to singular integrals 2000
1998 Lp Bounds for Singular Integrals and Maximal Singular Integrals with Rough Kernels.  Indiana University Mathematics Journal.  47:455-469. 1998

Research Overview

  • Analysis of Partial Differential Equations. More specifically:
    1) Soliton dynamics - linear and nonlinear stability of solitary waves in dispersive models, asymptotic stability. Existence and stability of solitary waves in spatially discrete systems. Analysis of waves in PT symmetric models.
    2) Local and global behavior of nonlinear dispersive PDE's - Schroedinger, wave, Klein-Gordon, Dirac, KdV, Ostrovsky/short pulse, Whitham etc. models.
    3) Well-posedness, regularity and asymptotics for fluid models: Boussinesq, quasi-geostrophic equation etc.

    • Teaching Overview

  • Undergraduate: Calculus - I, II, III; Linear algebra; Elementary ODE; Calculus of Variations; Applied PDE.
    Graduate: Mathematical Analysis - I, II; Measure theory; Complex Analysis; Advanced PDE; Functional Analysis I, II; Fourier analysis and PDE.

    • Teaching Activities

    Education And Training

  • Doctor of Philosophy in Mathematics, University of Missouri System : Columbia 1999

    • Full Name

  • Atanas Stefanov