email: vz@math.uiuc.edu

Publications

1. V. Zharnitsky, The Geometrical Description of the Nonlinear Dynamics of a Double Pendulum, SIAM J. Appl. Math. 55, 1753-1763, 1995.

2. V. Zharnitsky, Quasi-periodic motions in the billiard problem with a softened boundary,(PDF) Phys. Rev. Lett. 75, 4393-4396, 1995.

3. V. Zharnitsky, Breakdown of stability of motion in superquadratic potentials,(PDF) PhD Thesis , Rensselaer Polytechnic Institute, February 1996 and Commun. Math. Phys. 189, 165-204, 1997.

4. V. Zharnitsky, Resonances in a continuously forced anharmonic oscillator,(PDF) Phys. Lett. A 224, 264-270, 1997.

5. V. Zharnitsky, A note on adiabatic invariance in Hamiltonian systems depending singularly on the slow time, (PDF) Physica D 122, 62-72, 1998.

6. V. Zharnitsky, I. Mitkov, M. Levi, Parametrically Forced Sine-Gordon Equation and Domain Walls Dynamics in Ferromagnets, (PDF) Phys. Rev. B 57, 5033-35, 1998.

7. I. Mitkov, V. Zharnitsky, $\pi$-Kinks in the parametrically driven sine-Gordon equation and applications,(PDF) Physica D 123, 301-307, 1998.

8. V. Zharnitsky, Instability in Fermi-Ulam ``ping-pong'' problem,(PDF) Nonlinearity 11, 1481-87, 1998.

9. V. Zharnitsky, Quasiperiodic motions in the Hamiltonian systems of billiard type,(PDF) Phys. Rev. Lett. 81, 4839-42, 1998.

10. V. Zharnitsky, I. Mitkov, N. Gronbech-Jensen, $\pi$-kinks in strongly ac driven sine-Gordon systems, (PDF) Phys. Rev. E 58, R52-R55, 1998.

11. S. Turitsyn, A. Aceves, C.K.R.T. Jones, V. Zharnitsky, Average dynamics of the optical soliton in communication lines with dispersion management: Analytical results, (PDF) Phys. Rev. E 58, R48-R51, 1998.

12. Kim O. Rasmussen, V. Zharnitsky, I. Mitkov, N. Gronbech-Jensen, Higher order Shapiro steps in ac-driven Josephson junctions,(PDF) Phys. Rev. B 59, 58-61, 1999.

13. S. K. Turitsyn, A. B. Aceves, C.K.R.T. Jones, V. Zharnitsky, and V. K. Mezentsev, Hamiltonian averaging in soliton-bearing systems with a periodically varying dispersion, (PDF) Phys. Rev. E 59, R3843-R3846, 1999.

14. V. Zharnitsky, E. Grenier, S. K. Turitsyn, C.K.R.T. Jones, Jan S. Hesthaven, Ground states of the dispersion managed nonlinear Schroedinger equation, (PDF) Phys. Rev. E 62, November 2000.

15. V. Zharnitsky, E. Grenier, C.K.R.T. Jones, S. K. Turitsyn, Stabilizing effects of dispersion management, (PDF) Physica D 152-3, 794-817, 2001 (volume dedicated to Vladimir Zakharov on the occasion of his 60-th birthday)

16. V. Zharnitsky, Invariant tori in the Hamiltonian systems with impacts,(PDF) Commun. Math. Phys. 211, 289-302, 2000.

17. V. Zharnitsky, Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi-Ulam problem,(PDF) Nonlinearity 13, 1123-1136, 2000.

18. Y.M. Baryshnikov, V. Zharnitsky, Billiards and non-holonomic distributions, (PDF) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 300 (2003), Teor. Predst. Din. Sist. Spets. Vyp. 8, 56--64, 285.

19. V. Zharnitsky, Averaging for split-step scheme, (PDF) Nonlinearity 16, 1359-1366, 2003.

20. D.E. Pelinovsky, V. Zharnitsky, Averaging of dispersion managed solitons: existence, stability and propagation, (PDF) SIAM Jour. Appl. Math. 63, 745-776, 2003.

21. R. Jackson, C.K.R.T. Jones, V. Zharnitsky, Critical points in the averaged variational principle for Dispersion Managed Soliton, (PDF) Physica D 190, Issues 1-2, March 15, 63-77, 2004.

22. J.T. Moeser, C.K.R.T. Jones, V. Zharnitsky, Stable pulse solutions for the nonlinear Schroedinger equation with higher order dispersion management, (PDF), SIAM Jour. Math. Analysis. 35, Number 6, 1486-1511. 2004

23. Y.M. Baryshnikov, P. Heider, W. Parz, V. Zharnitsky, Whispering gallery modes inside the asymetric resonant cavities,( PDF) Phys. Rev. Lett. 93, 4839-42, 2004.

24. D.E. Pelinovsky, P.G. Kevrekidis, D.J. Frantzeskakis and V. Zharnitsky, Averaging for solitons with nonlinearity management revisited,( PDF) Phys. Rev. E 70, 2004.

25. M.I. Weinstein, V. Zharnitsky, A reaction dispersion system and Raman interactions, (PDF), SIAM Jour. Math. Analysis., 36, Number 6, 1742-1771. 2005.

26. M. Kunze, J. Moeser, V. Zharnitsky, Ground states for the higher order dispersion managed NLS equation in the absence of averaged dispersion, (PDF), Jour. Diff. Eq. 209, 77-100, 2005.

27. V. Zharnitsky, D.E. Pelinovsky, Averaging of nonlinearity managed pulses,( PDF) Chaos 15 (3): Art. No. 037105, 2005.

28. Y.M. Baryshnikov, V. Zharnitsky, Sub-Riemannian geometry and periodic orbits in classical billiards,( PDF) Mathematical Research Letters 13, no. 4, 587-598, 2006.

29. D. Hundertmark, V. Zharnitsky, On sharp Strichartz inequalities in low dimensions,( PDF) International Mathematics Research Notices, Vol. 2006, Art. ID 34080, 2006.

30. A. Tumanov, V. Zharnitsky, Periodic orbits in outer billiards,( PDF), International Mathematics Research Notices , vol. 2006, Article ID 67089, 17 pages, 2006

31. M.B. Erdogan, V. Zharnitsky, Quasi-linear dynamics in nonlinear Schrodinger equation with periodic boundary conditions, ( PDF), to appear in Communications in Mathematical Physics.

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