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Publications

Links point to an open-access or arXiv version whenever one is available; otherwise to the journal (DOI) page.

• A. Stefanov, M. Stanislavova, J. Cuevas-Maraver, P.G. Kevrekidis, On a Klein-Gordon reduction for oscillons, Journal of Nonlinear Waves, 2 (2026). [Open Access] [arXiv]
• M. Stanislavova, A. Stefanov, Asymptotic attraction with algebraic rates toward fronts of dispersive-diffusive Burgers equations, Journal of Nonlinear Waves, 1, no. 7 (2025). [Open Access] [arXiv]
• S. Hakkaev, M. Stanislavova, A. Stefanov, On the spectral instability of some cnoidal and snoidal waves of the full Klein-Gordon-Zakharov system, Dynamics of PDE, 22, no. 2 (2025), pp. 107-133. [Journal]
• S. Hakkaev, M. Stanislavova, A. Stefanov, Existence and stability for the traveling waves of the Benjamin equation, Nonlinearity, 38 (2025), 025020 (33pp). [Open Access] [arXiv]
• S. Hakkaev, M. Stanislavova, A. Stefanov, Spectral stability of periodic waves for the Zakharov system, J. Math. Phys. 64, no. 8 (2023). [arXiv] [Journal]
• M. Stanislavova, A. Stefanov, On the long time dynamics of the Landau-De Gennes gradient flow, Journal of Statistical Physics, 190, no. 1 (2023). [Journal]
• S. Hakkaev, M. Stanislavova, A. Stefanov, On the stability of the periodic waves for the Benney system, SIAM J. Appl. Dyn. Systems, 21, no. 3 (2022), pp. 1726-1747. [arXiv] [Journal]
• W. Feng, M. Stanislavova, A. Stefanov, On the Barashenkov-Bogdan-Zhanlav solitons and their stability, Chaos, Solitons and Fractals, Vol. 152 (2021), 111467. [arXiv] [Journal]
• S. Hakkaev, M. Stanislavova, A. Stefanov, On the stability of periodic waves for the cubic derivative NLS and the quintic NLS, Journal of Nonlinear Science, 31, no. 3 (2021). [arXiv] [Journal]
• H. Gaebler, M. Stanislavova, NLS and KdV Hamiltonian linearized operators: bounds on the spectra and optimal L² estimates for the semigroups, Physica D, Vol. 416 (2021), 132738. [PDF] [Journal]
• M. Stanislavova, A. Stefanov, Ground states for the nonlinear Schrödinger equation under a general trapping potential, Journal of Evolution Equations, 21, no. 1 (2021), pp. 671-697. [arXiv] [Journal]
• W. Feng, M. Stanislavova, On the spectral stability of standing waves of nonlocal PT-symmetric systems, in: Mathematics of Wave Phenomena, Trends in Mathematics, Birkhäuser (2020), pp. 145-162. [Journal]
• S. Malhi, M. Stanislavova, On the energy decay rates for the 1D damped fractional Klein-Gordon equation, Mathematische Nachrichten, 293, no. 2 (2020), pp. 363-375. [arXiv] [Journal]
• S. Hakkaev, M. Stanislavova, A. Stefanov, On the generation of stable Kerr frequency combs in the Lugiato-Lefever model of periodic optical waveguides, SIAM Journal of Applied Math, Vol. 79, No. 2 (2019), pp. 477-505. [arXiv] [Journal]
• A. Demirkaya, M. Stanislavova, Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation, DCDS-B, 24, no. 1 (2019), pp. 197-209. [Open Access] [PDF]
• M. Stanislavova, A. Stefanov, Asymptotic stability for spectrally stable Lugiato-Lefever solutions in periodic waveguides, Journal of Math Physics, 59, no. 10 (2018), 101502, 12pp. [Journal]
• S. Malhi, M. Stanislavova, When is the energy of the 1D damped Klein-Gordon equation decaying?, Mathematische Annalen, v. 372, 3-4 (2018), pp. 1459-1479. [PDF] [Journal]
• W. Feng, M. Stanislavova, On the vortices for the NLS in higher dimensions, Phil. Trans. R. Soc. A, v. 376 (2018), 20170189. [Open Access (PMC)] [Journal]
• W. Feng, M. Stanislavova, A. Stefanov, On the spectral stability of ground states of semi-linear Schrödinger and Klein-Gordon equations with fractional dispersion, Communications in Pure and Appl. Analysis, 17, no. 4 (2018), pp. 1371-1385. [Open Access] [PDF]
• M. Stanislavova, A. Stefanov, On the stability of standing waves for PT symmetric Schrödinger and Klein-Gordon equations in higher space dimensions, Proceedings of the AMS, 145 (2017), pp. 5273-5285. [Open Access] [PDF]
• S. Hakkaev, M. Stanislavova, A. Stefanov, Spectral stability for classical periodic waves of the Ostrovsky and short pulse models, Studies in Applied Math, 139, no. 3 (2017), pp. 405-433. [arXiv] [Journal]
• S. Hakkaev, M. Stanislavova, A. Stefanov, Periodic traveling waves of the regularized short pulse and Ostrovsky equations: existence and stability, SIAM Journal of Math Analysis, 49, no. 1 (2017), pp. 674-698. [PDF] [Journal]
• M. Stanislavova, A. Stefanov, On the spectral problem L u = λ u' and applications, Communications in Math Physics, v. 343, 2 (2016), pp. 361-391. [PDF]
• A. Demirkaya, P.G. Kevrekidis, M. Stanislavova, A. Stefanov, Spectral stability analysis for standing waves of a perturbed Klein-Gordon equation, DCDS-A (2015), pp. 359-368. [arXiv]
• A. Demirkaya, S. Hakkaev, M. Stanislavova, A. Stefanov, On the spectral stability of periodic waves of the Klein-Gordon equation, Diff. Int. Equations, V. 28, no. 5-6 (2015), pp. 431-454. [PDF]
• M. Stanislavova, Linear stability of solitary waves for the one-dimensional Benney-Luke and Klein-Gordon equations, Studies in Applied Mathematics, v. 134, no. 1 (2015), pp. 1-23. [PDF]
• A. Demirkaya, T. Kapitula, P.G. Kevrekidis, M. Stanislavova, A. Stefanov, On the spectral stability of kinks in some PT-symmetric variants of the classical Klein-Gordon field theories, Studies in Applied Mathematics, v. 133, 3 (2014), pp. 298-317. [arXiv]
• S. Hakkaev, M. Stanislavova, A. Stefanov, Linear stability analysis for periodic traveling waves of the Boussinesq equation and the KGZ system, Proc. Roy. Soc. Edinburgh A, v. 144, no. 3 (2014), pp. 455-489. [arXiv]
• M. Stanislavova, A. Stefanov, Spectral stability analysis for special solutions of second order in time PDE's: the higher dimensional case, Physica D, 262 (2013), pp. 1-13. [PDF]
• S. Hakkaev, M. Stanislavova, A. Stefanov, Spectral stability for traveling pulses of the Boussinesq 'abc' system, SIAM J. Appl. Dyn. Systems, v. 12, 2 (2013), pp. 878-898. [arXiv]
• S. Hakkaev, M. Stanislavova, A. Stefanov, Orbital stability for periodic standing waves of the Klein-Gordon-Zakharov system and the beam equation, ZAMP - Zeitschrift fuer Angewandte Mathematik und Physik, v. 64, 2 (2013), pp. 265-282. [PDF]
• M. Stanislavova, A. Stefanov, Linear stability analysis for traveling waves of second order in time PDEs, Nonlinearity v. 25 (2012), pp. 2625-2654. [arXiv]
• S. Hakkaev, M. Stanislavova, A. Stefanov, Transverse instability for periodic waves of KP-I and Schrödinger equations, Indiana Univ. Math. J. v. 61 (2012), pp. 461-492. [arXiv]
• A. Demirkaya, M. Stanislavova, Conditional stability theorem for the one dimensional Klein-Gordon equation, J. Math. Phys., 52 (2011). [PDF]
• M. Stanislavova, A. Stefanov, Asymptotic estimates and stability analysis of Kuramoto-Sivashinsky type models, Journal of Evolution Equations, 11 (2011), no. 3, pp. 605-635; Erratum: J. Evol. Equ. 11 (2011), no. 3, pp. 637-639. [PDF]
• A. Demirkaya, M. Stanislavova, Long time behavior for radially symmetric solutions of the Kuramoto-Sivashinsky equation, Dynamics of PDEs, v. 7, 2 (2010), pp. 161-175. [PDF]
• M. Stanislavova, A. Stefanov, Effective estimates of the higher Sobolev norms for the Kuramoto-Sivashinsky equation, DCDS (2009), pp. 729-738. [PDF] [arXiv]
• M. Stanislavova, A. Stefanov, On precise center stable manifold theorems for certain reaction-diffusion and Klein-Gordon equations, Physica D: Nonlinear Phenomena 238 (2009), pp. 2298-2307. [PDF]
• M. Stanislavova, Diffraction managed solitons with zero-mean diffraction, Journal of Dynamics and Differential Equations, 19 (2007), no. 2, pp. 295-307. [PDF]
• M. Stanislavova, A. Stefanov, Attractors for the viscous Camassa-Holm equation, DCDS-A 18 (2007), pp. 159-186. [arXiv]
• M. Stanislavova, On the global attractor for the damped BBM equation, Discrete and Continuous Dynamical Systems Suppl. Volume (2005), pp. 824-832. [PDF]
• M. Stanislavova, A. Stefanov, B. Wang, Asymptotic smoothing and attractors for the generalized Benjamin-Bona-Mahony equation on R³, J. Diff. Eq. 219 (2005), no. 2, pp. 451-483. [PDF]
• M. Stanislavova, Regularity of ground state solutions of dispersion managed nonlinear Schrödinger equations, J. Diff. Eq., 210, 1 (2005), pp. 87-105. [PDF]
• M. Stanislavova, A. Stefanov, On global finite energy solutions of the Camassa-Holm equation, Journal of Fourier Analysis and Applications 11 (2005), no. 5, pp. 511-531. [PDF]
• Y. Latushkin, C. Li, M. Stanislavova, The spectrum of a linearized 2D-Euler operator, Studies in Applied Mathematics, 112 (2004), pp. 259-270. [arXiv]
• F. Gesztesy, C.K.R.T. Jones, Y. Latushkin, M. Stanislavova, A spectral mapping theorem and invariant manifolds for nonlinear Schrödinger equations, Indiana Univ. Math. J., 49 (2000), pp. 221-243. [arXiv]
• M. Konstantinov, M. Stanislavova, P. Petkov, Perturbation bounds and characterization of the solution of the associated algebraic Riccati equation, Linear Algebra and its Applications, 285 (1998), pp. 7-31. [PDF]
• M. Stanislavova, A. Zhivkov, On the dynamics of the four dimensional rigid body in a quadratic potential field, J. Math. Phys. 36 (1995), pp. 5760-5788. [Journal]