A. Komech - Publications


Boussaid N., Komech A., Nabile Boussaid, Andrew Comech. On spectral stability of the nonlinear Dirac equation. http://arXiv.org/abs/1211.3336 http://arxiv.org/abs/1211.3336
Cuevas--Maraver J., Kevrekidis P.G., Saxena A., Cooper F., Khare A., Komech A., Bender C., Solitary waves of a PT-symmetric Nonlinear Dirac equation (with J. Cuevas--Maraver, P.G. Kevrekidis, A. Saxena, F. Cooper, A. Khare, and C. Bender). Journal of Selected Topics in Quantum Electronics (the IEEE Photonics Society), 22 (2016), no. 5, 1--9. DOI:10.1109/JSTQE.2015.2485607 http://arXiv.org/abs/1508.00852 http://dx.doi.org/10.1109/JSTQE.2015.2485607
Berkolaiko G., Komech A., Symmetry and Dirac points in graphene spectrum. http://arXiv.org/abs/1412.8096 http://arxiv.org/abs/1412.8096
Komech A., Phan T., Stefanov A., Asymptotic stability of solitary waves in generalized Gross--Neveu model. Annales de l"Institute Henri Poincaré (Analyse non linéaire). DOI:10.1016/j.anihpc.2015.11.001 http://dx.doi.org/10.1016/j.anihpc.2015.11.001 http://arXiv.org/abs/1407.0606 http://dx.doi.org/10.1016/j.anihpc.2015.11.001
Komech A., Global Attraction to Solitary Waves, chapter in the book Quantization, PDEs, and Geometry. The Interplay of Analysis and Mathematical Physics. Advances in Partial Differential Equations 251, 117--152. Birkhäuser, Berlin, 2015. ISBN 978-3-319-22407-7 http://www.springer.com/us/book/9783319224060
Berkolaiko G., Komech A., Sukhtayev A., Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields Nonlinearity 28 (2015), 577--592 DOI:10.1088/0951-7715/28/3/577 MR3311594 http://arxiv.org/abs/1306.5150 http://dx.doi.org/10.1088/0951-7715/28/3/577


Komech A., Guan M., Gustafson S., On linear instability of solitary waves for the nonlinear Dirac equation Annales de l"Institute Henri Poincaré (Analyse non linéaire), 31 (2014), 639--654 DOI:10.1016/j.anihpc.2013.06.001 MR3208458 http://arXiv.org/abs/1209.1146 http://dx.doi.org/10.1016/j.anihpc.2013.06.001


Komech A., Zubkov M., Polarons as stable solitary wave solutions to the Dirac-Coulomb system Journal of Physics A: Mathematical and Theoretical 46 (2013) 435201 (21pp) DOI:10.1088/1751-8113/46/43/435201 MR3118823 http://arXiv.org/abs/1207.2870 http://dx.doi.org/10.1088/1751-8113/46/43/435201
Komech A., Komech A., On the Titchmarsh convolution theorem for distributions on a circle. Journal of Functional Analysis and Its Applications, 47 (2013), 21--26 http://dx.doi.org/10.1007/s10688-013-0003-2
Komech A., Weak attractor of the Klein-Gordon field in discrete space-time interacting with a nonlinear oscillator. Discrete and Continuous Dynamical Systems -- Series A 33 (2013), no. 7, 2711--2755 http://dx.doi.org/10.3934/dcds.2013.33.2711


Komech A., On global attraction to solitary waves. Klein-Gordon field with mean field interaction at several points. Journal of Differential Equations, 252 (2012), 5390--5413. DOI:10.1016/j.jde.2012.02.001 http://dx.doi.org/10.1016/j.jde.2012.02.001
Berkolaiko G., Komech A., On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D. Mathematical Modelling of Natural Phenomena , Volume 7 (2012) Issue 02 , pp 13-31 Cambridge University Press DOI:10.1051/mmnp/20127202 http://arxiv.org/abs/0910.0917 http://dx.doi.org/10.1051/mmnp/20127202


Komech A., Komech A., On global attraction to quantum stationary states. Dirac equation with mean field interaction. Commun. Math. Anal. (2011), Conference 3, 131--136. http://arXiv.org/abs/0910.0517 http://math-res-pub.org/cma/proceedings/74-conference-3-cma
Komech A., Komech A., Well-posedness, energy and charge conservation for nonlinear wave equations in discrete space-time, Russian Journal of Mathematical Physics 18 (2011), no. 4, 410--419. DOI:10.1134/S1061920811040030 http://arxiv.org/abs/1008.3032 http://dx.doi.org/10.1134/S1061920811040030


Komech A., Komech A., Global attraction to solitary waves for nonlinear Dirac equation with mean field interaction, SIAM J. Math. Anal. 42 (2010), no. 6, 2944--2964. DOI:10.1137/090772125 http://dx.doi.org/10.1137/090772125
Komech A., Komech A., Global attractor for the Klein-Gordon field coupled to several nonlinear oscillators, Journal de Mathématiques Pures et Appliquées 93 (2010), no. 1, 91--111. DOI:10.1016/j.matpur.2009.08.011 http://arxiv.org/abs/math.AP/0702660 http://dx.doi.org/10.1016/j.matpur.2009.08.011


Komech A., Komech A., Global attraction to solitary waves for Klein-Gordon equation with mean field interaction. Annales de l"Institute Henri Poincaré (Analyse non linéaire) 26 (2009), no. 3, 855--868 http://dx.doi.org/10.1016/j.anihpc.2008.03.005
Komech A., Global Attraction to Solitary Waves (Habilitation), Technische Universität Darmstadt, Darmstadt, 2009 http://tuprints.ulb.tu-darmstadt.de/1411/
Komech A., Komech A., Principles of Partial Differential Equations, Springer, 2009. ISBN 978-1-4419-1095-0 http://dx.doi.org/10.2007/978-1-4419-1096-7


Komech A., Komech A., Global attraction to solitary waves in models based on the Klein-Gordon equation (review article). SIGMA 4 (2008), 010. 1--23. Proceedings of the Seventh International Conference ``Symmetry in Nonlinear Mathematical Physics"" (June 24-30, 2007; Institute of Mathematics, Kyiv, Ukraine). http://dx.doi.org/10.3842/SIGMA.2008.010


Komech A., Komech A., Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field. Arch. Ration. Mech. Anal. 185 (2007), no. 1, 105--142 http://dx.doi.org/10.1007/s00205-006-0039-z
Komech A., Cuccagna S., Pelinovsky D., Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation. SIAM J. Math. Anal. 39 (2007), no. 1, 1--33 http://dx.doi.org/10.1137/060651501
Komech A., Komech A., Global well-posedness for the Schrodinger equation coupled to a nonlinear oscillator. Russ. J. Math. Phys. 14 (2007), no. 2, 164--173 http://dx.doi.org/10.1134/S1061920807020057


Komech A., Cuevas J., Kevrekidis P., Discrete peakons (with Panos Kevrekidis and Jesus Cuevas), Phys. D 207 (2005), no. 3-4, 137--160 http://dx.doi.org/10.1016/j.physd.2005.05.019
Komech A., Rudenko S., Estimates on Level Set Integral Operators in Dimension Two (with Svetlana Roudenko), J. Geom. Anal. 15 (2005), no. 3, 405--423 http://dx.doi.org/10.1007/BF02930979


Komech A., Lp-Lq regularity of Fourier integral operators with caustics, Trans. Amer. Math. Soc. 356 (2004), no. 9, 3429--3454 http://dx.doi.org/10.1090/S0002-9947-04-03570-6


Komech A., Cuccagna S., On Lp continuity of singular Fourier Integral Operators (with Scipio Cuccagna), Trans. Amer. Math. Soc. 355 (2003), no. 6, 2453--2476 http://dx.doi.org/10.1090/S0002-9947-03-02929-5
Komech A., Type conditions and Lp-Lp, Lp-Lp" regularity of Fourier integral operators, Contemp. Math. 320 (2003), 91--109 http://dx.doi.org/10.1090/conm/320/05601


Komech A., Cuccagna S., Integral operators with two-sided cusp singularities (with Scipio Cuccagna), Internat. Math. Res. Notices 2000, no. 23, 1225--1242 http://dx.doi.org/10.1155/S107379280000061


Komech A., Optimal regularity of Fourier integral operators with one-sided folds, Comm. Partial Differential Equations 24 (1999), no. 7 & 8, 1263--1281 http://dx.doi.org/10.1080/03605309908821465


Komech A., Asymptotic Estimates for Oscillatory Integral Operators, PhD. Thesis. Columbia University, New York, 1997 http://app.cul.columbia.edu:8080/ac/handle/10022/AC:P:2850