Papers in refereed journals

1. 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. Available online. See also MPI Preprint 66/2007.
2. 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).
3. 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. See also MPI Preprint 85/2006.
4. 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. See also MPI Preprint 67/2006.
5. 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. See also MPI Preprint 121/2005.
6. 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.
7. Estimates on Level Set Integral Operators in Dimension Two (with Svetlana Roudenko), J. Geom. Anal. 15 (2005), no. 3, 405--423.
8. Discrete peakons (with Panos Kevrekidis and Jesus Cuevas), Phys. D 207 (2005), no. 3-4, 137--160.
9. Lp-Lq regularity of Fourier integral operators with caustics, Trans. Amer. Math. Soc. 356 (2004), no. 9, 3429--3454.
10. Purely nonlinear instability of standing waves with minimal energy (with Dmitry Pelinovsky), Comm. Pure Appl. Math 56 (2003), no. 11, 1565--1607.
11. Type conditions and Lp-Lp, Lp-Lp' regularity of Fourier integral operators, Contemp. Math. 320 (2003), 91--109.
12. On Lp continuity of singular Fourier Integral Operators (with Scipio Cuccagna), Trans. Amer. Math. Soc. 355 (2003), no. 6, 2453--2476
13. Integral operators with two-sided cusp singularities (with Scipio Cuccagna), Internat. Math. Res. Notices 2000, no. 23, 1225--1242
14. Optimal regularity of Fourier integral operators with one-sided folds, Comm. Partial Differential Equations 24 (1999), no. 7 & 8, 1263--1281.
15. Damping estimates for oscillatory integral operators with finite type singularities, Asymptot. Anal. 18 (1998), no. 3 & 4, 263--278.
16. Sobolev Estimates for Radon Transform of Melrose and Taylor, Comm. Pure Appl. Math 51 (1998), no. 5, 537--550.
17. 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
18. Oscillatory Integral Operators in Scattering Theory, Comm. Partial Differential Equations 22 (1997), 841--867.

Miscellaneous

1. Book of Practical PDEs (with Alexander Komech). MPI Lecture Note 33/2007.
2. Cotlar-Stein Almost Orthogonality Lemma, lecture note. Columbia University, New York, 1997.

Keywords

AMS Subject Classification

• 37K40 Soliton theory, asymptotic behavior of solutions
• 37L30 Attractors and their dimensions, Lyapunov exponents
• 35B41 Attractors
• 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics
• 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

ACKNOWLEDGMENT: The papers on this site are the product of the research which has been partially supported by the National Science Foundation under Grants DMS-9970330/0296036, DMS-0200880/0434698/0621257, and DMS-0600863.