[1]
**
Self-focusing and Modulational Analysis of Nonlinear Schroedinger
Equations
**

* Ph.D. Thesis, New York University, (1982) *

[2]
**
Nonlinear Schroedinger equations and sharp interpolation
estimates
**

* Commun. Math. Phys.*, Volume 87 (1983) 567-576.

[3]
**
Focusing singularity for the nonlinear Schroedinger equation
**

(with D. W. McLaughlin and G. C. Papanicolaou)
*
North Holland Math. Studies*, Volume 81 (1983)

[4]
**
Modulational stability of ground states of nonlinear Schroedinger
equations
**

*
SIAM J. Math. Anal.* Volume 16 (1985) 472--491.

[5]
**
Hill's equations with a large potential
**

(with J. B. Keller)
*
SIAM J. Appl. Math.* Volume 45 (1985) 200--214.

[6]
**
Lyapunov stability of ground states of nonlinear dispersive
evolution equations
**

*
Comm. Pure Appl. Math.*, Volume 39 (1986) 51--68

[7]
**
On the solitary wave of the generalized Korteweg-de Vries
equation**

* in Nonlinear Systems of Partial Differential Equations,
AMS Lectures in Applied Mathematics*, Volume 23 (1986) 23--30.

[8]
** On the structure and formation of singularities in solutions of
nonlinear dispersive evolution equations **

*
Comm. Partial Diff. Eqns.*,
Volume 11 (1986) 545--565.

[9]
**
The nonlinear Schroedinger limit of the Zakharov equations
governing plasma turbulence **

(with S. H. Schochet)
* Commun. Math.
Phys.* Volume 106 (1986) 569--580

[10]
**
Remarks on orbital stability of ground states for subcritical and
critical nonlinearities**

*
in Semigroups, Theory and Applications,
Vol I (H. Brezis, M. G. Crandall and F. Kappel, eds.),
Pitman
Res. Notes Math. Ser.*, Volume 141 (1986) 249--252.

[11]
** A stable manifold theorem for the curve shortening equation
**

(with C. L. Epstein)
*
Comm. Pure Appl. Math.*, Volume 40 (1987) 119--139.

[12]
** Existence and dynamic stability of solitary wave solutions of
equations governing long wave propagation **

* Comm. Partial Diff. Eqns.*,
Volume 12 (1987) 1133--1173.

[13]
**
Asymptotic behavior of stability regions of Hill's equation
**

(with J. B. Keller)
*
SIAM J. Appl. Math.*, Volume 47 (1987) 941--958.

[14]
**
Solitary waves of nonlinear dispersive evolution equations with
critical power nonlinearities
**

* J. Differential Equations*, Volume 69 (1987)
192--203.

[15]
**
Remarks on the Morse index of ground states of semilinear elliptic
variational problems
**

* (1987), preprint
*

[16]
**
On the bound states of the nonlinear Schroedinger equation with a
linear potential
**

(with H. A. Rose)
*
Physica D.*, Volume 30 (1988) 207--218.

[17]
**
Ground states of nonlinear dispersive equations: stability and
singularities
**

* in Nonlinear Partial Differential Equations and
Their Applications,
College de France Lectures
(Paris 1984-1985), Pitman Res. Notes Math. Ser.*,

Volume 166 (1988) 214--220.

[18]
**
The nonlinear Schroedinger equation: singularity formation,
stability and dispersion
**

* Contemp. Math. *, Volume 99 (1989) 213--232.

[19]
**
Multichannel nonlinear scattering for nonintegrable systems
**

* in
Proceedings of Conference on an Integrable and Nonintegrable
Systems, June, 1988, Oleron, France, Integrable Systems and
Applications, Springer Lecture Notes in Physics*, Volume 342

[20]
**
Bound states of Zakharov's model with a linear potential in three
dimensions and the
collapse of Langmuir waves
**

(with D. DuBois, H. Rose, D. Russel)

[21]
**
Multichannel nonlinear scattering in nonintegrable systems
**

(with A. Soffer)
* Commun. Math. Phys*, Volume 133 (1990) 119--146.

[22]
**
On the vortex solutions of some nonlinear scalar field equations
**

* Rocky Mountain J. Math.*, Volume 21 (1991) 821--827.

[23]
**
Dispersion of low energy to the generalized Korteweg-de Vries
equation
**

(with F. M. Christ)
* J. Funct. Anal.* Volume 100 (1991) 87--109.

[24]
**
On asymptotic stability of solitary waves
**

(with R.L. Pego)
*
Phys. Lett. A.* Volume 162 (1992) 263--268.

[25]
**
Multichannel nonlinear scattering and stability II. The case of
Anisotropic and potential and data
**

(with A. Soffer)
* J. Differential Equations*, Volume 98 (1992) 376--390.

[26]
**
Eigenvalues, instabilities of solitary waves
**

(with R.L. Pego)
* Phil. Trans. Royal Soc. London,
Series A*, Volume 340 (1992) 47--94.

[27]
** Evans' Function, Melnikov's Integral, and Solitary Wave Instabilities
**

(with R.L. Pego)
* in Mathematics in Science and Engineering, Volume 192,
Differential Equations with Applications to
Mathematical Physics;
Proceedings of GITUAB Conference on
Differential Equations and Mathematical
Physics, March, 1992,
ed. W.F. Ames, E.M Harrell II, and
J.V. Herod, Academic Press 1993.
*

[28]
** Oscillatory instability of traveling waves for a KdV - Burgers equation
**

(with P. Smereka, and R.L. Pego)
* Physica D,* Volume 67 (1993) 45--65.

[29]
**
Asymptotic stability of solitary waves
**

(with R.L. Pego)
* Commun. Math. Phys.* Volume 164 (1994) 305--349.

[30]
**
Oscillatory instability of solitary waves in a continuum model of
lattice vibrations
**

(with R.L. Pego and P. Smereka)
* Nonlinearity* Volume 8 (1996) 921--941.

[31]
** Convective stability of Boussinesq solitary waves
**

(with R.L. Pego)
* Studies in Applied Mathematics* Volume 99 (1997) 311--375.

[32]
** Asymptotic stability of solitary waves of the Regularized
Long Wave
Equation
**

(with J.R. Miller)
* Commun. Pure Appl. Math.*
Volume 49 (1996), no. 4, 399--441.

[33]
** On strong spectral stability of solitary waves
**

(with R.L. Pego)
* Proceedings of IUTAM
Symposium on Nonlinear Waves in Fluids, Hannover, Germany - 1994.
*

[34]
**
On the ground states of vector nonlinear Schroedinger
equation
**

(with T. Colin)
* Annales de L'Institut Henri Poincar'e (Physique
Th'eorique),* Volume 65, No. 1 (1996), 57--79.

[35]
**
Dynamic stability of vortex solutions of Ginzburg Landau
and Nonlinear Schroedinger equations
**

(with J. Xin)
*
Commun. Math. Phys.* Volume 180,
(1996) 389--428.

[36]
**
Soliton dynamics in the discrete nonlinear
Schroedinger equations,
**

(with B. Malomed)
* Phys. Lett. A *
Volume 220 (1996)\ 91-96.

[37]
**
Time dependent resonance theory and perturbations of
embedded eigenvalues
**

(with A. Soffer)
*
in
Proceedings of Conference on Partial Differential Equations and
Applications,
Toronto
June 1995, CRM Lecture notes. Eds. P. Greiner, V. Ivrii,
L. Seco and C. Sulem
*

[38]
**
Asymptotic stability of nonlinear bound states in
conservative dispersive systems
**

* in Mathematical Problems in the Theory on Nonlinear
Hydrodynamics Waves, eds. F. Dias, J.-M. Ghidaglia & J.-C. Saut,
Contemp. Math.* Volume 200
(1996) AMS.

[39]
**
Excitation and dynamics of pulses in coupled fiber
arrays
**

(with B. Yeary)
*
Phys. Lett. A* Volume 222 (1996) 157--162

[40]
**
Modelocking pulse dynamics in a fiber laser with a
saturable Bragg reflector
**

(with J.N. Kutz, B.C. Collings,
K. Bergman, S. Tsuda, S.T. Cundiff, W.H.
Knox, & P. Holmes)

* Journal of the Optical Society of America B* Volume
14 #10 (1997) 2681-2690.

[41]
**
Resonances, radiation damping, and instability of
Hamiltonian nonlinear waves
**

(with A. Soffer)
* Inventiones Mathematicae *,
Volume 136 (1999) 9-74.

[42]
**
Nonautonomous Hamiltonians
**

(with A. Soffer)
*Journal of Statistical Physics*,
Volume 93 (1998) 359--391.

[43]
**
Time dependent resonance theory
**

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

[44]
**
Excitation Thresholds for Nonlinear Localized Modes on Lattices
**

*Nonlinearity* Volume 12 (1999) 673-691.

[45]
**
Ionization and scattering for short lived potentials
**

(with A. Soffer)
* Lett. Math. Phys.* Volume 48 (1999)

[46]
**
Radiation induced instability in interconnected systems
**

(with A. Bloch and P. Hagerty)
* Proc. of the 38th
Conf. on Decisions and Control, IEEE* (2000)

[47]
**
Parametrically excited Hamiltonian Partial Differential
Equations
**

(with E. Kirr)
*SIAM J. Math. Anal.* Volume 33 (2001) 16-52.

[48]
**
Metastability of breather modes of time dependent potentials
**

(with P.D. Miller and A. Soffer)
*Nonlinearity* Volume 13 (2000) 507--568.

[49]
**
Dynamics of lattice kinks
**

(with P. Kevrekidis)
*Physica D* Volume 142 (2000) 113-152.

[50]
**
Nonlinear propagation of light in one-dimensional periodic structures
**

(with R. Goodman and P. Holmes)
*J. Nonlinear Sci.* Volume 11 (2001) 123-168.

[51]
**
Theory of nonlinear pulse propagation periodic structures
**

(with A. Aceves and C.M. de Sterke)
*in * Nonlinear Photonic Crystals,

* B. Eggleton and
R.E. Slusher, eds. Springer Verlag (2003) *

[52]
**
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

[53]
**
Mathematical frontiers in optical solitons
**

(with J. Bronski and M. Segev)
*Proc. Natl. Acad. Sci. USA* Volume 98 No. 23 (2001) 12872-12873.

[54]
**
Stopping light on a defect
**

(with R.H. Goodman and R.E. Slusher)
*Journal of the Optical Society B* Volume 19 No. 7 (2002) 1635-1652.

[55]
**
Selection of the ground state for nonlinear Schroedinger equations
**

(with A. Soffer)
* Reviews in Mathematical Physics, Volume 16, #8, (2004) 977-1071
arXiv.org/abs/nlin/0308020
*

[56]
**
Radiation induced instability
**

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

[57]
**
Breathers on a Background: Periodic and quasiperiodic solutions of
extended
discrete nonlinear wave systems
**

(with P. Kevrekidis)

of the journal Mathematics and Computers in Simulation

[58]
**
Metastable states in parametrically excited multimode Hamiltonian systems
**

(with E. Kirr)
*Commun. Math. Phys., Volume 236, 335-372, 2003 *

[59]
**
Diffusion of power in randomly perturbed Hamiltonian partial differential equations
**

(with E. Kirr)
* Commun. Math. Phys. volume 255, 293--328 (2005)*

[60]
**
Interaction of NLS solitons with defects:
Numerical experiments and
finite dimensional modeling
**

(with R.H. Goodman and P.J. Holmes)

a conference in honor of Klaus Kirchg"assner's 70th birthday, Kloster Irsee, Germany, Jan 6-10, 2002.

[61]
**
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) *

[62]
**
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)*

[63]
**
Resonances of microstructured photonic waveguides and
higher order homogenization expansion
**

(with S. Golowich)
* Physica B, Volume 338 136-142 (2003)*

[64]
**
Theory and computation of scattering resonances of microstuctures
**

(with S. Golowich)
*Waves in Periodic and Random Media, ed. P. Kuchment
Contemporary Mathematics, Volume 339, AMS, 2003 *

[65]
**
A Reaction Dispersion System and Raman Interactions
**

(with V. Zharnitsky)
* SIAM J. Math. Analysis, Volume 36 No. 6, 1742--1771 (2005) *

[66]
**
Scattering resonances of microstructures and homogenization theory
**

(with S. Golowich)
* SIAM J. Multiscale Modeling and Simulation, volume 3 No.3, 477-521
(2005)*

[67]
**
Strong NLS Soliton-Defect Interactions
**

(with R.H. Goodman and P.J. Holmes)
*Physica D volume 161, 21-44 (2004)*

[68]
**
Geometric analysis of bifurcation and symmetry breaking in a Gross-Pitaevskii
Equation
**

(with R.K. Jackson)
* J. Stat. Physics volume 116 881-905 (2004)*

[69]
**
Extended Hamiltonian Systems
**

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

[70]
**
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*

[71]
**
Trapping Light with Grating Defects
**

(with R.H. Goodman, R.E. Slusher and M.Klaus)
* Contemp. Math. Volume 379 (2005) 83--92*

[72]
**
Wave dynamics in optically modulated waveguide arrays
**

(with M. Ablowitz, K. Julien and Z. Musslimani)
*Phys. Rev. E volume 71 (2005) 055602(R) *

[73]
**
Transient radiative behavior of Hamiltonian systems in finite domains
**

(with P.G. Kevrekidis and Z. Rapti)
* Phys. Lett A volume 345 (2005) 1--9*

[74]
**
Theory of nonlinear dispersive waves and selection of the ground state
**

(with A. Soffer)
* Phys. Rev. Lett. volume 95, 213905 (2005)*

[75]
**
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) *

[76]
**
Waves in nonlinear microstructures - Ultra-short pulses and Bose-Einstein
Condensates
**

(with G. Fibich and Y. Sivan)
*Physical Review Letters, Volume 97, 193902 (2006)*

[77]
**
Degenerate dispersive equations arising in the study of magma dynamics
**

(with G. Simpson and M. Spiegelman)
* Nonlinearity, Volume 20, 21--49 (2007)*

[78]
**
Resonance Problems in Photonics,
**

Invited Review and Plenary Lecture at International Symposium on the Frontiers
of Applied Mathematics,

Tsinghua University, Beijing, 2006,
*in Frontiers of Applied Mathematics, World Scientific (2007)*

[79]
**
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)*

[80]
**
Cloaking via change of variables in electric impedance tomography
**

(with R.V. Kohn, H. Shen, M.S. Vogelius)
* Inverse Problems, Volume 24, 015016 (2008) *

[81]
**
Optimization of scattering resonances,**

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

*http://www.springerlink.com/content/020274566m8r6494/fulltext.pdf*

[82]
**
Stability and instability of nonlinear defect states in the coupled mode equations
--- analytical and numerical study
**

(with R.H. Goodman)

DOI information: 10.1016/j.physd.2008.04.009

[83]
**
On a Hamiltonian PDE arising in magma dynamics
**

(with G. Simpson and P. Rosenau)

* Discrete and Continuous Dynamical Systems - B, volume 10 (4), 2008
*

[84]
**
Asymptotic stability of ascending solitary magma waves,
**

(with G. Simpson)

*SIAM J. Math. Analysis Volume 40, Issue 4, pp. 1337-1391 (2008), http://arxiv.org/abs/0801.0463*

[85]
**
Qualitative and quantitative analysis of stability and instability dynamics of
positive lattice solitons
**

(with Y. Sivan, G. Fibich and B. Ilan)
* Physical Review E Volume 78, No.4 (2008)
DOI: 10.1103/PhysRevE.78.046602*

[86]
**
Dynamics of Nonlinear Schr\"odinger \ Gross-Pitaevskii Equations;
Mass Transfer in Systems with Solitons and Degenerate Neutral Modes
**

(with Z. Gang)

[87]
**
A Multiscale Model of Partial Melts I.: Effective Equations
**

(with G. Simpson and M. Spiegelman)
* J. Geophys. Res., 115, B04410 (2010); doi:10.1029/2009JB006375
*

[88]
**
A multiscale model of partial melts II.: Computational studies
**

(with G. Simpson and M. Spiegelman)
* J. Geophys. Res., 115, B04411 (2010); doi:10.1029/2009JB006376 *

[89]
**
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)*

[90]
**
Band edge solitons, nonlinear Schroedinger / Gross-Pitaevskii equations and effective media
**

(with B. Ilan) * SIAM J. Multiscale Model. and Simul., 8, No. 4, 1055--1101
(2010)
*

[91]
**
Long time dynamics near the symmetry breaking bifurcation for nonlinear Schr\"odinger / Gross-Pitaevskii equations
**

(with J. Marzuola)
* Discrete and Continuous Dynamical Systems- A, Volume 28, #4, 1505--1554 (2010)
*

[92]
**
Wave operator bounds for 1-dimensional Schr\"odinger operators with singular pot
entials and applications
**

(with V. Duchene and J. Marzuola)
*Journal of Math. Physics Volume 52, 013505 (2011)*

[93]
**
Radiative Decay of Bubble Oscillations in a Compressible Fluid
**

(with A.M. Shapiro)
* SIAM J. Math. Analysis Volume 43, 828-876 (2011) *

[94]
**
Defect modes and homogenization of periodic Schr\"odinger operators
**

(with M. Hoefer)
* SIAM J. Mathematical Analysis Volume 43, 971-996 (2011)*

[95]
**
Equipartition of energy in Nonlinear Schroedinger / Gross-Pitaevskii Equations
**

(with Z. Gang)
* Applied Math. Research Express (AMRX), 2011 --
doi:10.1093/amrx/abr001 *

[96]
**
Coherent structures and carrier shocks in the nonlinear periodic Maxwell equations
**

(with G. Simpson)
* SIAM J. Multiscale Model. and Simul. 9, pp. 955-990 (2011)
-- http://arxiv.org/abs/1009.3675 *

[97]
**
Scattering, homogenization and interface effects for oscillatory potentials with strong singularities
**

(with V. Duchene)
* SIAM J. Multiscale Model. and Simul. 9 pp. 1017-1063 (2011)
-- http://arxiv.org/abs/1010.2694 *

[98]
**
Emergence of Periodic Structure from Maximizing the Lifetime of a Bound State Coupled to Radiation
**

(with B. Osting)
* SIAM J. Multiscale Model. and Simul. 9, No. 2 pp. 654-685 (2011)
-- http://arxiv.org/abs/1010.5746 *

[99]
**
Polychromatic Solitons in a Periodic and Nonlinear Maxwell Equation
**

(with D. Pelinovsky and G. Simpson)
* SIAM J. Appl. Dyn. Syst. 11, pp. 478-506 (2012)
*

[100]
**
Honeycomb Lattice Potentials and Dirac Points
**

(with C.L. Fefferman)
*J. Amer. Math. Soc. 25 (2012), pp. 1169-1220
http://dx.doi.org/10.1090/S0894-0347-2012-00745-0
*

[101]
**
Waves in Honeycomb Structures
**

(with C.L. Fefferman)
* Journees Equations aux derivees partialles, Biarretz, 3-7 juin 2012, GDR 243
4 (CNRS) -- http://arxiv.org/abs/1212.6684
*

[102]
**
Long-Lived Scattering Resonances and Bragg Structures
**

(with B. Osting)
* SIAM J. Applied Math. Vol. 73, #2 (2013) -- DOI: 10.1137/110856228
*

[103]
**
Resonances of a potential well with a thick barrier
**

(with D. Dobson, F. Santosa and S. Shipman)
* SIAM J. Applied Math. Volume 73, #4 (2013) - DOI: 10.1137/120883694
*

[104]
**
The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension
**

(with O. Costin and S. Tanveer)
*SIAM J. Math. Analysis Volume 45, #5 (2013) -- DOI: 10.1137/120892659
*

[105]
**
Wave packets in honeycomb structures and two-dimensional Dirac equations
**

(with C.L. Fefferman)
* Commun. Math. Phys. Volume 326, 251--286, (2014) --
DOI 10.1007/s00220-013-1847
-2
*

[106]
**
****
A variational perspective on cloaking by anomalous localized resonance
**

(with R.V. Kohn, J.Lu and B. Schweizer)
* Communications in Mathematical Physics (2014) -- 10.1007/s00220-014-1943-y
*

[107]
**
Scattering and Localization Properties of Highly Oscillatory Potentials
**

(with V. Duchene and I. Vukicevic)
* Commun. Pure Appl. Math. volume 67, 0083-0128 (2014)
*

[108]
**
Homogenized description of defect modes in periodic structures with localized defects
**

(with V. Duchene and I. Vukicevic)
* Commun. Math. Sci. Vol. 13, No. 3, pp. 777-823 (2015)
*

[109]
**
Self-trapping and Josephson tunneling solutions to the nonlinear Schr\"odinger / Gross-Pitaevskii equation
**

(with R.H. Goodman and J.L. Marzuola) * Discrete and Continuous Dynamical Systems - A, Vol. 35, No. 1 (2015), 225-246
*

[110]
**
Localized states and their dynamics in the nonlinear Schroedinger / Gross-Pitaeveskii equation: Analysis and Applications
**

Frontiers in Applied Dynamics: Reviews and Tutorials, volume 3 (Springer, 2015)
* Invited Review
*

[111]
**
Topologically protected states in one-dimensional
continuous systems and Dirac points **

(with C.L. Fefferman and J.P. Lee-Thorp)

* Proceedings of the National Academy of Sciences (2014),
http://www.pnas.org/content/111/24/8759.full *

[112]
**
On-site and off-site solitary waves of the discrete nonlinear Schroedinger equation in multiple dimensions**

(with M. Jenkinson)

*Nonlinearity Volume 29, Number 1 (2016) http://arxiv.org/abs/1405.3892*

[113]
**
Oscillatory and localized perturbations of periodic structures and the bifurcation of defect modes
**

(with V. Duchene and I. Vukicevic)

*SIAM J. Math. Anal. 47(5) (2015) 3832--388*

[114]
**
Mathematical Challenges and Opportunities in Optics and Photonics**

(with G. Bao)

* SIAM News, May 1, 2015 *

[115]
**
Photonic realization of topologically protected bound states in
domain-wall modulated waveguide arrays**

(with J. P. Lee-Thorp, I. Vukicevic, X. Xu, J. Yang, C. L. Fefferman and C. W. Wong
)

* Phys. Rev. A 93 (2016) 033822*

[116]
**
Edge states in honeycomb structures**

(with C.L. Fefferman and J.P. Lee-Thorp)

* Annals of PDE (2016) 2:12*

[117]
**
Bifurcations of edge states -- topologically protected
and non-protected -- in continuous 2D honeycomb
structures**

(with C.L. Fefferman and J.P. Lee-Thorp)

*
2D Materials, Volume 3 No. 1, 2016*

[118]
**
****
Discrete Solitary Waves in Systems with Nonlocal Interactions and the Peierls-Nabarro Barrier **

(with M. Jenkinson)

Communications in Mathematical Physics (2017) DOI: 10.1007/s00220-017-2839-4

[119]
**
Topologically protected states in one-dimensional
systems**

(with C.L. Fefferman and J.P. Lee-Thorp)

* Memoirs of the American Mathematical Society (2017)
ISBN: 978-1-4704-2323-0;
http://bookstore.ams.org/memo-247-1173*

[120]
**
Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature
**

(with A.B. Watson and J. Lu)

Journal of Mathematical Physics 58, 021503 Physics (2017)

doi: http://dx.doi.org/10.1063/1.4976200

[121]
**
Honeycomb Schroedinger operators in the strong binding regime
**

(with C.L. Fefferman and J.P. Lee-Thorp)

Communications in Pure and Applied Mathematics, Volume 71 #6 (2018) 1178-1270

(https://arxiv.org/abs/1610.04930)

[122]
**
Wavepackets in inhomogeneous periodic media: propagation through a one-dimensional band crossing
**

(with A.B. Watson)

Communications in Mathematical Physics, volume 363 (2018) 655-698

(https://arxiv.org/abs/1709.05575)

[123]
**
Spectral band degeneracies of pi/2 - rotationally invariant periodic Schroedinger operators
**

Multiscale Modeling and Simulation, volume 16 #4 (2018) 1684-1731

**
Erratum, (3 pages)
**
Multiscale Model. Simul., 18 #3 (2020) 1371 - 1373.

(with R.T. Keller, J.L. Marzuola and B. Osting)

[124]
**
Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene
**

(with J.P. Lee-Thorp and Y. Zhu)

Archives for Rational Mechanics and Analysis, volume 232 (2019) 1-63

(https://arxiv.org/abs/1710.03389)

[125]
**
Edge states and the Valley Hall Effect**

(with A. Drouot)

Advances in Mathematics volume 368 (2020) 107142

[126]
**
Dirac operators and domain walls**

(with J. Lu and A. Watson)

SIAM J. Math. Analysis, 52 (2), (2020) 1115-1145

https://arxiv.org/abs/1808.01378

[127]
**
Edge States of continuum Schroedinger operators for sharply terminated honeycomb structures**

(with C.L. Fefferman)

Communications in Mathematical Physics, 380, 853-945 (2020)

https://arxiv.org/abs/1810.03497

[128]
**
Defect modes for dislocated periodic media**

(with A. Drouot and C.L. Fefferman)

Communications in Mathematical Physics, 377, 1637-1680 (2020)

https://arxiv.org/abs/1810.05875

[129]
**
TE band structure for high contrast honeycomb media **

(with M. Cassier)

International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2020

[130]
**
Landau levels in strained two-dimensional photonic crystals**

(with J. Guglielmon and M. Rechtsman)

Physical Review A 103, 013505 (2021)

[131]
**
Lower Bound on Quantum Tunneling for Strong Magnetic Fields **

(with C.L.Fefferman and J. Shapiro), SIAM J. Mathematical Analysis
Vol. 54, #1 2022

[132]
**
Tight binding reduction and topological equivalence in strong magnetic fields **

(with J. Shapiro), Advances in Mathematics Volume 403, 108343 2022

[133]
**
High contrast elliptic operators in honeycomb structures **

(with M. Cassier), Multiscale Modeling and Simulation Vol. 19, #4 2022

[134]
**
Effective gaps in continuous Floquet Hamiltonians **

(with A. Sagiv), SIAM J. Mathematical Analysis Vol. 54, #1 2022

[135]
**
Is the continuum SSH model topological? **

(with J. Shapiro), J. Math. Phys. 63, 111901 (2022); https://doi.org/10.1063/5.0064037

[136]
**
Edge states in rationally terminated honeycomb structures **

(with C.L. Fefferman and S. Fliss), Proc. Nat. Acad. Sci. (2022)

[137]
**
Discrete honeycombs, rational edges and edge states **

(with C.L. Fefferman and S. Fliss), Communications on Pure and Applied Mathematics, 2023

[138]
**
Radiative decay of edge states in Floquet media **

(with S.N. Hameedi and A. Sagiv), Multiscale Modeling and Simulation, Vol. 21, Iss. 3 (2023)

[139]
**
Discrete Breathers of Nonlinear Dimer Lattices: Bridging the Anti-continuous and Continuous Limits **

(with A. Hofstrand and H. Li), Journal of Nonlinear Science, Vol. 33 (2023)

[140]
**
Free boundary problem for a gas bubble in a liquid, and asymptotic stability of the manifold of spherically symmetric equilibria **

(with C.C. Lai), Archive for Rational Mechanics and Analysis volume 247, 100 (2023)

[141]
**
Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array **

(with Q. Du, H. Li and L. Zhang), to appear in the Journal of Scientific Computing

[142]
**
Near invariance of quasi-energy spectrum of Floquet Hamiltonians **

(with A. Sagiv), submitted

[143]
**
Thermal relaxation toward equilibrium and periodically pulsating bubbles in an
incompressible liquid **

(with C.-C. Lai), Nonlinear Analysis
Volume 238, January 2024, 113397

[144]
**
Direct Observation of Landau Levels in Silicon Photonic Crystals**

(with M. Barsukova, F. Grise, Z. Zhang, S. Vaidya, J. Guglielmon, L. He, B. Zhen, R. McEntaffer, M. C. Rechtsman), Nature Photonics vol. 18 (2024)

[145]
**
Nonlocal PDEs and Quantum Optics: Bound States and Resonances**

(with E. Hiltunen, J. Kraisler and J. Schotland), SIAM J. Math.Anal. 56 (2024) 3, 3802-3831

[146]
**
Dispersive decay estimates for Dirac equations with a domain wall**

(with J. Kraisler and A. Sagiv), to appear in SIAM J. Math. Analysis

[147]
**
Charge transfer plasmonics in bespoke graphene/alpha Cl_3 cavities**

(with Vitalone, Rocco; SÃ¸rensen Jessen, Bjarke; Jing, Ran; Rizzo, Daniel; Xu, Suheng; Hsieh, Valerie; Cothrine, Matthew;

Mandrus, David; Wehmeier, Lukas; Carr, G. Lawrence; Bisogni, Valentina; Dean, Cory; Hone, James;

Liu, Mengkun; Fogler, Michael; Basov, Dimitri), to appear in ACS Nano

[148]
**
Stability of traveling waves in a nonlinear hyperbolic system approximating a dimer array of oscillators**

(with A. Hofstrand and H. Li), submitted

[149]
**
Instability of quadratic band degeneracies and the emergence of Dirac
points**

(with J. Chaban), submitted

[150]
**
Asymmetric deformations of a perturbed spherical bubble in an incompressible fluids**

(with C.-C. Lai), submitted