Recent Papers

* Resonances, Radiation Damping, and Instability of Hamiltonian Nonlinear Waves
(with A. Soffer) Inventiones Mathematicae , Volume 136 (1999) 9-74.

* Nonautonomous Hamiltonians
(with A. Soffer) Journal of Statistical Physics, Volume 93, (1998) 524-545.

* Time Dependent Resonance Theory
(with A. Soffer) Geometrical and Functional Analysis, Volume 8, (1998) 1086-1128.

* Excitation Thresholds for Nonlinear Localized Modes on Lattices
Nonlinearity Volume 12 (1999) 673-691.

* Ionization and Scattering for Short Lived Potentials
(with A. Soffer) Letters in Mathematical Physics Volume 48 (1999) 339-352

* Radiation induced instability in interconnected systems
(with A. Bloch and P. Hagerty) Proc. of the 38th Conf. on Decisions and Control, IEEE

* Metastability of Breather Modes of Time Dependent Potentials (pdf)
(with P.D. Miller and A. Soffer) Nonlinearity Volume 13 (2000) 507-568.

* Dynamics of lattice kinks
(with P. Kevrekidis) Physica D Volume 142 (2000) 113-152.

* Breathers on a Background: Periodic and Quasiperiodic Solutions of Extended Discrete Nonlinear Wave Systems
(with P. Kevrekidis) to appear in the Special Issue of Mathematics and Computers in Simulation dedicated to the 2nd IMACS Nonlinear Waves Conference

* Parametrically excited Hamiltonian Partial Differential Equations
(with E. Kirr) SIAM J. Math. Anal. Volume 33 (2001) 16-52.

* Nonlinear propagation of light in one-dimensional periodic structures
(with R. Goodman and P. Holmes) J. Nonlinear Sci. Volume 11 (2001) 123-168.

* Theory of nonlinear pulse propagation periodic structures
(with A. Aceves and C.M. de Sterke) Nonlinear Photonic Crystals,
B. Eggleton and R.E. Slusher, eds. Springer Verlag

* Mathematical Frontiers in Optical Solitons (pdf)
(with J. Bronski and M. Segev) Proc. Natl. Acad. Sci. USA Volume 98 No. 23 (2001) 12872-12873. Errata

* Stopping light on a defect (pdf)
(with R.H. Goodman and R.E. Slusher) Journal of the Optical Society B Volume 19 No. 7 (2002) 1635-1652. Errata (reference numbering)

* Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model
(with R.H. Goodman and P.J. Holmes) Physica D, Volume 161 (2002) 21-44

* Metastable states in parametrically excited multimode Hamiltonian systems
(with E. Kirr) Commun. Math. Phys., Volume 236, 335-372 (2003)

* Selection of the ground state for nonlinear Schroedinger equations
(with A. Soffer) Reviews in Mathematical Physics, Volume 16, #8, (2004) 977-1071

* Radiation induced instability
(with P. Hagerty and A.M. Bloch) SIAM J. Appl. Math. Volume 64, No. 2 484--524 (2003)

* Interaction of NLS solitons with defects: Numerical experiments and finite dimensional modeling
(with P.J. Holmes and R.H. Goodman) Invited paper for Mathematics as a Guide to the Understanding of Applied Nonlinear Problems, a conference in honor of Klaus Kirchg\"{a}ssner's 70th birthday, Kloster Irsee, Germany, Jan 6-10, 2002,

* Homogenization expansion for resonances of microstructured photonic waveguides
(with S. Golowich) Journal of the Optical Society of America B, volume 20, No. 4, 633-647, 2003

* Gyroscopically stabilized classical and quantum oscillators and heat baths
(with A.M. Bloch, P. Hagerty and A.G. Rojo) J. Stat. Phys, 115, 1073-1100 (2004)

* Resonances of microstructured photonic waveguides and higher order homogenization expansion
(with S. Golowich) Physica B, Volume 338 136-142 (2003)

* Theory and computation of scattering resonances of microstuctures
(with S. Golowich) Waves in Periodic and Random Media, ed. P. Kuchment, Contemporary Mathematics volume 339 (2003) AMS

* Strong NLS Soliton-Defect Interactions
(with R.H. Goodman and P.J. Holmes) Physica D 161, 21-44 (2004)

* A reaction dispersion system and Raman interactions
(with V. Zharnitsky) SIAM J. Math. Anal. no. 6 1742--1771 (2005)

* Scattering resonances of microstructures and homogenization theory
(with S. Golowich) SIAM J. Multiscale Modeling and Simulation, volume 3 No.3 (2005)

* Diffusion of power in randomly perturbed Hamiltonian partial differential equations
(with E. Kirr) Commun. Math. Phys. volume 255, 293-328 (2005)

* Geometric analysis of bifurcation and symmetry breaking in a Gross-Pitaevskii Equation
(with R.K. Jackson) J. Stat. Physics volume 116, 881-905 (2004)

* Extended Hamiltonian Systems
in Handbook of Dynamical Systems, eds. B. Hasselblatt and A. Katok, volume 1B, North Holland, 2005

* Spontaneous Symmetry Breaking in Photonic Lattices: Theory and Experiment
(with P.G. Kevrekidis, Z. Chen, B.A. Malomed and D.J. Frantzeskakis) Phys. Lett. A volume 340 (2005) 275-280

* Wave dynamics in optically modulated waveguide arrays
(with M. Ablowitz, K. Julien and Z. Musslimani) Phys. Rev. E volume 71 (2005) 055602(R)

* Transient radiative behavior of Hamiltonian systems in finite domains
(with P.G. Kevrekidis and Z. Rapti) Phys. Lett. A volume 345 (2005) 1--9

* Bound states of nonlinear Schr\"odinger equations with periodic nonlinear microstructure
(with G. Fibich and Y. Sivan) Physica D, Volume 217, no. 1, 31--57 (2006)

* Theory of nonlinear dispersive waves and selection of the ground state
(with A. Soffer) Physical Review Letters, Volume 95, 213905 (2005)

* Waves in nonlinear microstructures - Ultra-short pulses and Bose-Einstein Condensates
(with G. Fibich and Y. Sivan) Physical Review Letters, Volume 97, 193902 (2006)

* Degenerate dispersive equations arising in the study of magma dynamics
(with G. Simpson and M. Spiegelman) Nonlinearity, Volume 20, 21--49 (2007)

* Resonance Problems in Photonics
Invited Review and Plenary Lecture at International Symposium on the Frontiers of Applied Mathematics,
Tsinghua University, Beijing, 2006, in Frontiers in Applied Mathematics, World Scientific (2007)

* Symmetry breaking in the nonlinear Schroedinger / Gross-Pitaevskii equation
(with E.W. Kirr, P. Kevrekides and E. Shlizerman) SIAM J. Math. Anal. Volume 40, Issue 2, pp. 566-604 (2008)

* Cloaking via Change of Variables in Electric Impedance Tomography
(with R.V. Kohn, H. Shen, M.S. Vogelius and M.I. Weinstein) Inverse Problems, Volume 24, 015016 (2008)

* Optimization of scattering resonances
(with P. Heider, D. Berebichez and R.V. Kohn) Structural and Multidisciplinary Optimization (2008) 36:443-456.

* Asymptotic stability of ascending solitary magma waves
(with G. Simpson) SIAM J. Math. Analysis Volume 40, Issue 4, pp. 1337-1391 (2008)

On a Hamiltonian PDE arising in magma dynamics
(with G. Simpson and P. Rosenau)
Discrete and Continuous Dynamical Systems - B, volume 10 (4), 2008
http://arxiv.org/abs/0801.0555

* Stability and instability of nonlinear defect states in coupled mode equations-- analytical and numerical study
(with R.H. Goodman) Physica D: Nonlinear Phenomena 237 (2008), pp. 2731-2760
DOI information: 10.1016/j.physd.2008.04.009

* Qualitative and quantitative analysis of stability and instability dynamics of p ositive lattice solitons
(with Y. Sivan, G. Fibich and B. Ilan) Physical Review E Volume 78, No.4 (2008)
URL: http://link.aps.org/abstract/PRE/v78/e046602 DOI: 10.1103/PhysRevE.78.046602

Dynamics of Nonlinear Schr\"odinger \ Gross-Pitaevskii Equations;
Mass Transfer in Systems with Solitons and Degenerate Neutral Modes

(with Z. Gang) Analysis and Partial Differential Equations, Volume 1, No. 3, 2008

A Multiscale Model of Partial Melts 1: Effective Equations
(with G. Simpson and M. Spiegelman) J. Geophys. Res., doi:10.1029/2009JB006375, in press.

A Multiscale Model of Partial Melts 2: Numerical Results
(with G. Simpson and M. Spiegelman) J. Geophys. Res., doi:10.1029/2009JB006376, in press.

Cloaking via change of variables for the Helmholtz equation
(with R.V. Kohn, D. Onofrei and M. Vogelius), Commun. Pure Appl. Math., 63, 973-1016 (2010)

Band edge solitons, nonlinear Schroedinger - Gross Pitaevskii equation and effective media
(with B. Ilan) SIAM J. Multiscale Model. and Simul., 8, No. 4, 1055--1101 (2010)

Long time dynamics near the symmetry breaking bifurcation for nonlinear Schr\"od inger / Gross-Pitaevskii equations
(with J. Marzuola) Discrete and Continuous Dynamical Systems, Volume 28, #4, 1505--1554 (2010)

Radiative Decay of Bubble Oscillations in a Compressible Fluid
(with A. Shaw-Krauss) submitted, 2010

Defect modes and homogenization of periodic Schr\"odinger operators
(with M. Hoefer) submitted, 2010 p>

Coherent structures and carrier shocks in the nonlinear periodic Maxwell equations
(with G. Simpson) submitted, 2010