Books

1. Principles of Partial Differential Equations (with Alexander Komech). Springer, 2009. ISBN 978-1-4419-1095-0. Available at Amazon.com. DOI: 10.2007/978-1-4419-1096-7

Dissertations

1. Global Attraction to Solitary Waves, Habilitation. Technische Universität Darmstadt, Darmstadt, 2009.
2. Asymptotic Estimates for Oscillatory Integral Operators, PhD. Thesis. Columbia University, New York, 1997. See also local copy.

Recent papers

1. Weak attractor of the Klein-Gordon field in discrete space-time interacting with a nonlinear oscillator, submitted.
2. On global attraction to solitary waves. Klein-Gordon field with mean field interaction at several points. Journal of Differential Equations, to appear. DOI: 10.1016/j.jde.2012.02.001
3. On the meaning of the Vakhitov-Kolokolov stability criterion for the nonlinear Dirac equation. arXiv:1107.1763. Mathematical Modelling of Natural Phenomena (2012), to appear.
4. On spectral stability of solitary waves of nonlinear Dirac equation on a line (with Gregory Berkolaiko), arXiv:0910.0917. Mathematical Modelling of Natural Phenomena (2012), to appear.
5. On the Titchmarsh convolution theorem for distributions on a circle (with Alexander Komech). arXiv:1108.2463. Journal of Functional Analysis and Applications, to appear.

Papers in refereed journals

1. Well-posedness, energy and charge conservation for nonlinear wave equations in discrete space-time (with Alexander Komech), Russian Journal of Mathematical Physics 18 (2011), no. 4, 410--419. DOI: 10.1134/S1061920811040030. See also arXiv:1008.3032.
2. On global attraction to quantum stationary states. Dirac equation with mean field interaction (with Alexander Komech), Commun. Math. Anal. (2011), Conference 3, 131--136. Available online: math-res-pub.org, arXiv:0910.0517.
3. Global attraction to solitary waves for nonlinear Dirac equation with mean field interaction (with Alexander Komech), SIAM J. Math. Anal. 42 (2010), no. 6, 2944--2964. DOI: 10.1137/090772125.
4. Global attractor for the Klein-Gordon field coupled to several nonlinear oscillators (with Alexander Komech), Journal de Mathématiques Pures et Appliquées 93 (2010), no. 1, 91--111. DOI: 10.1016/j.matpur.2009.08.011. See also MPI Preprint 17/2007.
5. Global attraction to solitary waves for Klein-Gordon equation with mean field interaction (with Alexander Komech). Annales de l'Institute Henri Poincaré (Analyse non linéaire) 26 (2009), no. 3, 855--868. DOI: 10.1016/j.anihpc.2008.03.005. See also MPI Preprint 66/2007.
6. Global attraction to solitary waves in models based on the Klein-Gordon equation (review article) (with Alexander Komech). 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). DOI: 10.3842/SIGMA.2008.010
7. Global well-posedness for the Schrodinger equation coupled to a nonlinear oscillator (with Alexander Komech), Russ. J. Math. Phys. 14 (2007), no. 2, 164--173. DOI: 10.1134/S1061920807020057. See also MPI Preprint 85/2006.
8. Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation (with Scipio Cuccagna and Dmitry Pelinovsky), SIAM J. Math. Anal. 39 (2007), no. 1, 1--33. DOI: 10.1137/060651501. See also MPI Preprint 67/2006.
9. Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field (with Alexander Komech), Arch. Ration. Mech. Anal. 185 (2007), no. 1, 105--142. DOI: 10.1007/s00205-006-0039-z. See also MPI Preprint 121/2005.
10. On global attraction to solitary waves for the Klein-Gordon equation coupled to nonlinear oscillator (with Alexander Komech), C. R. Math. Acad. Sci. Paris 343 (2006), no. 2, 111--114. DOI: 10.1016/j.crma.2006.06.009
11. Estimates on Level Set Integral Operators in Dimension Two (with Svetlana Roudenko), J. Geom. Anal. 15 (2005), no. 3, 405--423. DOI: 10.1007/BF02930979
12. Discrete peakons (with Panos Kevrekidis and Jesus Cuevas), Phys. D 207 (2005), no. 3-4, 137--160. DOI: 10.1016/j.physd.2005.05.019
13. Lp-Lq regularity of Fourier integral operators with caustics, Trans. Amer. Math. Soc. 356 (2004), no. 9, 3429--3454. DOI: 10.1090/S0002-9947-04-03570-6
14. Purely nonlinear instability of standing waves with minimal energy (with Dmitry Pelinovsky), Comm. Pure Appl. Math 56 (2003), no. 11, 1565--1607. DOI: 10.1002/cpa.10104
15. Type conditions and Lp-Lp, Lp-Lp' regularity of Fourier integral operators, Contemp. Math. 320 (2003), 91--109. DOI: 10.1090/conm/320/05601
16. On Lp continuity of singular Fourier Integral Operators (with Scipio Cuccagna), Trans. Amer. Math. Soc. 355 (2003), no. 6, 2453--2476. DOI: 10.1090/S0002-9947-03-02929-5
17. Integral operators with two-sided cusp singularities (with Scipio Cuccagna), Internat. Math. Res. Notices 2000, no. 23, 1225--1242. DOI: 10.1155/S107379280000061
18. Optimal regularity of Fourier integral operators with one-sided folds, Comm. Partial Differential Equations 24 (1999), no. 7 & 8, 1263--1281. DOI: 10.1080/03605309908821465
19. Damping estimates for oscillatory integral operators with finite type singularities, Asymptot. Anal. 18 (1998), no. 3 & 4, 263--278.
20. Sobolev Estimates for Radon Transform of Melrose and Taylor, Comm. Pure Appl. Math 51 (1998), no. 5, 537--550. DOI: 10.1002/(SICI)1097-0312(199805)51:5<537::AID-CPA4>3.0.CO;2-9
21. Integral operators with singular canonical relations, chapter (pp. 200--248) in a book Spectral Theory, Microlocal Analysis, Singular Manifolds (M. Demuth, E. Schrohe, B.-W. Schulze, J. Sjostrand, eds.). Akademie Verlag, Berlin, 1997. ISBN 978-3527401208
22. Oscillatory Integral Operators in Scattering Theory, Comm. Partial Differential Equations 22 (1997), 841--867. DOI: 10.1080/03605309708821286