Publications
- S. Hakkaev, M. Stanislavova, A. Stefanov, On the instability of the cnoidal and snoidal
waves of the full Klein-Gordon-Zakharov system, submitted.
- S. Hakkaev, M. Stanislavova, A. Stefanov, All non-vanishing bell-shaped solitons for the
cubic derivative NLS are stable, submitted.
- W. Feng, M. Stanislavova, A. Stefanov, On the Barashenkov-Smirnov solitons and their
stability, submitted.
- H. Gaebler, M. Stanislavova, NLS and KdV Hamiltonian linearized operators: bounds on the spectra
and optimal $L^2$
estimates for the semigroups, Physica D, Vol. 416, (2021), 132738.
- M. Stanislavova, A. Stefanov, Ground states for the nonlinear Schrödinger equation under
a general trapping potential, Journal of Evolution Equations, online first (2020).
- W. Feng, M. Stanislavova, On the spectral stability of standing waves of nonlocal PT -
symmetric systems, special volume "Mathematics of Wave Phenomena", (2020).
- S. Malhi, M. Stanislavova, On the energy decay rates for the 1D damped fractional Klein-Gordon equation,
Mathematische Nachrichten, 293, no 2 (2019), pp 363-375.
- 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.
- A. Demirkaya, M. Stanislavova, Numerical results on existence and stability of standing
and traveling waves for the fourth order beam equation, DCDS- B, 24 (1), (2019), pp
159-186.
- M. Stanislavova, A. Stefanov, Asymptotic stability for spectrally stable Lugiato-Lefever
solutions in periodic waveguides, Journal of Math Physics, 59, 10 (2018), 101502, 12pp.
- 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.
- W. Feng, M. Stanislavova, On the vortices for the NLS in higher dimensions, Phil Trans
A, v. 376 (2018), 20170189.
- W. Feng, M. Stanislavova, A. Stefanov, On the spectral stability of ground states of the
semi-linear Schrödinger and Klein-Gordon equations with fractional dispersion, Communications in Pure and Appl. Analysis 17, no. 4, (2018), p. 1371-1385.
- 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) p. 5273-5285.
- 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),
p. 405-433.
- 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), p. 674-698.
- M. Stanislavova, A. Stefanov, On the spectral problem $L u=\lambda u'$ and applications, Communications in Math Physics, v. 343, 2, (2016), p. 361-391.
- A. Demirkaya, P.G. Kevrekidis, M. Stanislavova, A. Stefanov, Spectral stability analysis
for standing waves of a perturbed Klein-Gordon equation, DCDS - A (2015) p.359-368.
- 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), 431-454.
- 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), 1-23.
- A. Demirkaya, T. Kapitula, P.G. Kevrekidis, M. Stanislavova and 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), p.298-317.
- 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. 114, no. 3 (2014), p. 455-489.
- 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), p.1-13.
- 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), p.878-898.
- 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) p. 265-282.
- M. Stanislavova, A. Stefanov , Linear stability analysis for traveling waves of second
order in time PDEs, Nonlinearity v. 25, (2012) p. 2625-2654.
- S. Hakkaev, M. Stanislavova, A. Stefanov, Transverse instability for periodic waves of
KP-I and Schrödinger equations, Indiana Univ. Math. J. v.61 (2012), 461-492.
- A. Demirkaya, M. Stanislavova , Conditional stability theorem for the one dimensional
Klein-Gordon equation, J. Math. Phys., 52, (2011).
- M. Stanislavova, A. Stefanov , Asymptotic estimates and stability analysis of Kuramoto-Sivashinsky type models, Journal of Evolution Equations (JEE), 11(2011), no. 3, 605-
635, Erratum: J. Evol. Equ. 11 (2011), no. 3, 637-639.
- A.Demirkaya, M. Stanislavova, Long time behavior for radially symmetric solutions
of the Kuramoto-Sivashinsky equation, Dynamics of PDEs, v.7, 2 (2010), 161-175.
- M. Stanislavova, A. Stefanov, Effective estimates of the higher Sobolev norms for the
Kuramoto-Sivashinsky equation, DCDS (2009), 729-738.
- M. Stanislavova, A. Stefanov, On precise center stable manifold theorems for certain
reaction-diffusion and Klein-Gordon equations, Physica D: Nonlinear Phenomena 238 (2009)
2298-2307.
- M. Stanislavova, Diffraction managed solitons with zero-mean diffraction, Journal of
Dynamics and Differential Equations, 19 (2007), no.2, 295-307.
- M. Stanislavova, A. Stefanov, Attractors for the viscous Camassa-Holm equation, DCDS
- A 18 (2007), 159-186.
- M. Stanislavova, On the global attractor for the damped BBM equation, Discrete and
Continuous Dynamical Systems Suppl. Volume (2005), 824-832.
- M. Stanislavova, A. Stefanov, B. Wang, Asymptotic smoothing and attractors for the
generalized Benjamin-Bona-Mahony equation on $R^3$, J.Diff. Eq. 219 (2005), no. 2,
451-483.
- M. Stanislavova, Regularity of ground state solutions of dispersion managed nonlinear Schrödinger equations, J.Diff. Eq., 210, 1
(2005) 87-105.
- M. Stanislavova, A. Stefanov, On global finite energy solutions of the Camassa-Holm
equation, Journal of Fourier Analysis and Applications 11 (2005), no. 5, 511-531.
- Y. Latushkin, C.Li and M. Stanislavova, The spectrum of a linearized 2D-Euler operator, Studies in Applied Mathematics, 112 (2004) 259-270.
- F. Gesztesy, C.K.R.T. Jones, Y. Latushkin and M. Stanislavova, A spectral mapping
theorem and invariant manifolds for nonlinear Schrödinger equations, Indiana Univ.
Math. J.,49 (2000) 221-243.
- M. Konstantinov, M. Stanislavova, P.Petkov, Perturbation bounds and characterization
of the solution of the associated algebraic Riccati equation. Journal of Linear Algebra
and Applications, 285 (1998) 7-31.
- M. Stanislavova, A. Zhivkov, On the dynamics of the four dimensional rigid body in
a quadratic potential field, J. Math. Phys. 36 (1995), 5760-5788.