[1]
Self-focusing and Modulational Analysis of Nonlinear Schr\"odinger
Equations
Ph.D. Thesis, New York University, (1982)
[2]
Nonlinear Schr\"odinger equations and sharp interpolation
estimates
Commun. Math. Phys., Volume 87 (1983) 567-576.
[3]
Focusing singularity for the nonlinear Schr\"odinger equation
(with D. W. McLaughlin and G. C. Papanicolaou)
North Holland Math. Studies, Volume 81 (1983)
[4]
Modulational stability of ground states of nonlinear Schr\"odinger
erequations
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 (1985) 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 Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger 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)
(1989) preprint.
[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 Schr\"odinger
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 Schr\"odinger equations
(with J. Xin)
Commun. Math. Phys. Volume 180,
(1996) 389--428.
[36]
Soliton dynamics in the discrete nonlinear
Schr\"odinger 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 (1997)
[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
[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 Schr\"odinger equations
(with A. Soffer)
to appear in Reviews in Mathematical Physics
arXiv.org/abs/nlin/0308020
(110 page manuscript)
[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)
in Special Issue "Nonlinear Waves: Computation and Theory II"
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)
to appear in Communications in Mathematical Physics
[60]
Interaction of NLS solitons with defects:
Numerical experiments and
finite dimensional modeling
(with R.H. Goodman and P.J. Holmes)
Invited paper for Mathematics as a Guide to the Understanding
of Applied Nonlinear Problems, 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)
to appear in SIAM J. Math. Analysis
[66]
Scattering resonances of microstructures and homogenization theory
(with S. Golowich)
to appear in SIAM Journal on Multiscale Modeling and Simulation
[67]
Strong NLS Soliton-Defect Interactions
(with R.H. Goodman and P.J. Holmes)
Physica D 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
to appear 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)
submitted