Papers of Michael I. Weinstein

[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) (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 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

[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) 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) 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) 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.

[82] Stability and instability of nonlinear defect states in the 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

[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),

[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) Analysis and Partial Differential Equations, volume 1, No. 3, 2008

[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) --

[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) --

[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) --

[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

[101] Waves in Honeycomb Structures
(with C.L. Fefferman) Journees Equations aux derivees partialles, Biarretz, 3-7 juin 2012, GDR 243 4 (CNRS) --

[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),

[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)

[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--3883

[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;

[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)

[121] Honeycomb Schroedinger operators in the strong binding regime
(with C.L. Fefferman and J.P. Lee-Thorp)
to appear in Communications in Pure and Applied Mathematics

[122] Wavepackets in inhomogeneous periodic media: propagation through a one-dimensional band crossing
(with A.B. Watson)

[123] Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene
(with J.P. Lee-Thorp and Y. Zhu)

[124] Spectral band degeneracies of pi/2 - rotationally invariant periodic Schroedinger operators
(with R.T. Keller, J.L. Marzuola and B. Osting)