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uw.eduIn Preparation and Submitted Manuscripts
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E. Shlizerman, V. Rom-Kedar and A. Soffer Localization in the perturbed periodic Nonlinear Schrödinger equation in preparation. |
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E. Shlizerman and V. Rom-Kedar, Mixing of resonant modes in the Faraday surface waves experiment to be submitted. |
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E. Shlizerman and V. Rom-Kedar, Classification of solutions of the forced periodic nonlinear Schrödinger equation submitted. |
Publications
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E. Shlizerman and V. Rom-Kedar, Parabolic Resonance: A Route to Hamiltonian Spatio-Temporal Chaos Physical Review Letters, 102, 033901 (2009). Abstract: We show that small asymetric initial data near an unperturbed stable plane wave can evolve into a regime of spatio-temporal chaos in the slightly forced conservative periodic one-dimensional nonlinear Schrödinger equation. |
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E.W. Kirr, P. Kevrekides, E. Shlizerman and M.I. Weinstein Symmetry Breaking Bifurcation in the Nonlinear Schrödinger - Gross-Pitaevskii Equations SIAM J. Math. Anal. (SIMA), Volume 40, Issue 2, pp. 566-604 (2008). Abstract: We consider a class of nonlinear Schrödinger / Gross-Pitaveskii (NLS-GP) equations, i.e. NLS with a linear potential. NLS-GP plays an important role in the mathematical modeling of nonlinear optical as well as macroscopic quantum phenomena (BEC). We obtain conditions for a symmetry breaking bifurcation in a symmetric family of states as N, the squared L2 norm (particle number, optical power), is increased.... |
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E. Shlizerman and V. Rom-Kedar, Three types of chaos in the forced nonlinear Schrödinger equation Physical Review Letters, 96, 024104 (2006). Abstract: Three different types of chaotic behavior and instabilities (homoclinic chaos, hyperbolic resonance and parabolic resonance) in Hamiltonian perturbations of the nonlinear Schrrödinger (NLS) are described. The analysis is performed on a truncated model using a novel framework in which a hierarchy of bifurcations is constructed. ... Pdf | Journal | Webpage (includes Movies) |
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E. Shlizerman and V. Rom-Kedar, Characterization of Orbits in the Truncated Nonlinear Schrödinger Model ENOC-2005, Fifth EUROMECH Nonlinear Dynamics Conference. Abstract: The truncated and forced non-linear Schrödinger (NLS) model is analyzed using a novel framework in which a hierarchy of bifurcations is constructed. Consequently, a classification of the types of instabilities which are expected to appear due to the forcing is provided;... A simple statistical measure which distinguishes between the fundamentally different types of instabilities is proposed. ... Pdf | Updated | Webpage |
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E. Shlizerman and V. Rom-Kedar, Hierarchy of bifurcations in the truncated and forced NLS model CHAOS, 15(1), March, 2005. Abstract: The truncated forced non-linear Schrödinger (NLS) model is known to mimic well the forced NLS solutions in the regime at which only one linearly unstable mode exists. Using a novel framework in which a hierarchy of bifurcations is constructed, we analyze this truncated model and provide insights regarding its global structure and the type of instabilities which appear in it. ... Pdf | Journal | Webpage |
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E. Shlizerman and V. Rom-Kedar, Energy surfaces and Hierarchies of bifurcations - Instabilities in the forced truncated NLS In Proceedings of the International Summer School on Chaotic Dynamics and Transport in Classical and Quantum Systems. October, 2004. Abstract: A two-degrees of freedom near integrable Hamiltonian which arises in the study of low-amplitude near-resonance envelope solutions of the forced Sine-Gordon equation is analyzed. The energy momentum bifurcation diagrams and the Fomenko graphs are constructed ... Pdf | Book on Amazon | Webpage |
Selected Presentations
| E. Shlizerman and V. Rom-Kedar, Parabolic Resonance - A Route to Spatio Temporal Chaos, SIAM Conference on Applications of Dynamical Systems, Snowbird - Utah, USA, May, 2009. * Received "SIAM Student Travel Award" at DS'09. |
| E. Shlizerman and V. Rom-Kedar, From Order to Spatiotemporal Chaos in the Perturbed NLS, Applied Mathematics Seminar, Tel Aviv University, May, 2009. |
| E. Shlizerman and V. Rom-Kedar, From Order to Spatiotemporal Chaos in the Perturbed NLS, Applied Mathematics Colloquium, Columbia University, Jan, 2009, Lefschetz Center for Dynamical Systems Seminar, Brown University, Feb, 2009, Dynamical Systems Seminar, UCSB, Feb, 2009. |
| E. Shlizerman and V. Rom-Kedar, Parabolic Resonance- A Route to Spatio Temporal Chaos, Workshop on Stability and Instability in Mechanical Systems: Applications and Numerical Tools, Barcelona, Dec, 2008. |
| E. Shlizerman and V. Rom-Kedar, Instabilities in the Forced Periodic Non-linear Schrödinger Equation - Part II (Spatio Temporal chaos), SIAM Conference on Nonlinear Waves and Coherent Structures, Rome, July, 2007. |
| E. Shlizerman and V. Rom-Kedar, Resonant Surface Waves - new theory of old experiments, Sixth Negev Workshop on Applied Mathematics, Blaustein Institute For Advanced Studies in Mathematics, Sede-Boqer Campus, July, 2007. |
| E. Shlizerman and V. Rom-Kedar, Resonant Surface Waves - new theory of old experiments, SIAM Conference on Applications of Dynamical Systems, Snowbird - Utah, USA, May, 2007. * Chair of concurrent session (CP1) on "Dynamics of Waves". |
| E. Shlizerman and V. Rom-Kedar, Classifying chaos in the forced nonlinear Schrödinger equation, Applied Mathematics Seminar, Columbia University, New York, July, 2006. |
| E. Shlizerman and V. Rom-Kedar, Mechanisms of chaos in the forced nonlinear Schrödinger equation, Israeli Applied Math. Workshop, Tel Aviv University, Israel, January, 2006. ppt |
| E. Shlizerman and V. Rom-Kedar, Instabilities in the Forced and Truncated Non-linear Schrödinger Equation, SIAM Conference on Applications of Dynamical Systems, Snowbird - Utah, USA, May, 2005. ppt * Received "SIAM Student Travel Award" at DS'05. |
| E. Shlizerman and V. Rom-Kedar, Instabilities in the Forced and Truncated Non-linear Schrödinger Equation, Israeli Applied Math. Workshop, Bar-Ilan University, Israel, December, 2004. ppt |
| E. Shlizerman and V. Rom-Kedar, Energy surfaces and Hierarchies of bifurcations, International Summer School on Chaotic Dynamics and Transport in Classical and Quantum Systems, Cargese, France, August, 2003. ppt |
Theses
| MSc thesis - Thesis (pdf) | Presentation (ppt) |