**PUBLICATIONS**

**DAVID W. McLAUGHLIN**

**_____________________________________________________________**

**ARTICLES**

1.
"The Phase Shift,
II. As a Continuous Functional'' (with W. Frank), J. Math. Phys. **12**,
2525-2529 (1971).

2.
"Path Integrals
in Curved Spaces'' (with L. S. Schulman), J. Math. Phys. **12**, 2520-2524
(1971).

3.
"Path Integrals, Asymptotics, and Singular Perturbations'', J. Math. Phys. **13**,
784-796 (1972).

4.
"Complex Time,
Contour Independent Path Integrals, and Barrier Penetration'', J. Math. Phys. **13**,
1099-1108 (1972).

5.
"A Stochastic
Gaussian Beam'' (with R. Burridge and G. Papanicolaou), J. Math. Phys. **14**, 84-89; Erratum in
Vol. 14 (1973).

6.
"The Solution by
Descent of Certain Partial Differential Equations on the Sphere and Lobachevsky Plane'' (with R. Burridge
and G. Papanicolaou), Comm. Pure. Appl.
Math. **26**, 105-129 (1973).

7.
"The Soliton: A New Concept in Applied Science'' (with A. C.
Scott and F. Y. F. Chu), Proc. IEEE **61**, 1443-1483 (1973). (Translated
into Russian as an Appendix of the book "Active and Nonlinear Wave
Propagation in Electronics").

8.
"A Restricted Backlund Transformation'' (with A. C. Scott), J. Math.
Phys. **14**, 1817-1828 (1973).

9.
"Semiclassical Radiation Theory and the Inverse Method''
(with J. Corones), Phys. Rev. A. **10**, 2051-2062
(1974).

10.
"A Stochastic Gaussian
Beam II'', J. Math. Phys. **16**, 100-103 (1975).

11.
"Four Examples of
the Inverse Method as a Canonical Transformation'', J. Math. Phys. **16**,
96-99; Erratum in 16, 1704 (1975).

12.
"The Feynman
Integral'' (with J. B. Keller), Amer. Math. Monthly **82**, 451-465 (1975).

13.
"Some Comments on
Backlund Transformations, Canonical Transformations,
and the Inverse Scattering Method'' (with H. Flaschka),
Springer Lecture Notes in Math. **515**, 253-295 (1975).

14.
"Quantum Theory
of a Swept Gain Amplifier II'' (with F. A. Hopf and
P. Meystre), Phys. Rev. A **13**, 777-783 (1976).

15.
"Canonically
Conjugate Variables for the Korteweg-de Vries Equation and Toda Lattice with Periodic Boundary
Conditions'' (with H. Flaschka), Prog.
in Theor. Phys. **55**,
438-456 (1976).

16.
"Solitons under Perturbations'' (with J. P. Keener), Phys.
Rev. A **16**, 777-790 (1977); Erratum in 17, 1555 (1977).

17.
"A Green's
Function for a Linear Equation Associated with Solitons''
(with J. P. Keener), J. Math. Phys. **18**, 2008-2013 (1977).

18.
"Fluxon Interactions'' (with A. C. Scott), Appl. Phys. Lett. **30**,
545-547 (1977).

19.
"Aspects of Soliton Physics'' (with G. L. Lamb, Jr.), Volume **17**
"Solitons" ed. R. K. Bullough
and P. J. Caudrey, (Springer Verlag,
1980).

20.
"Exact Solutions
of the Sine-Gordon Equation'' (with G. Costabile, R. Costabile, R. Parmentier, B. Savo, and A. C. Scott), Appl.
Phys. Lett. **32**, 587-589 (1978).

21.
"Perturbation
Analysis of Fluxon Dynamics'' (with A. C. Scott),
Phys. Rev. A. **18**, 1652-1680 (1978).

22.
"Multiphase
Averaging and the Inverse Spectral Solution of KdV''
(with H. Flaschka and **33**, 739-784 (1980).

23.
"On Davydov's Alpha Helix Solitons''
(with J. Hyman and A. C. Scott), Physica D **3**,
23-44 (1981).

24.
"Modulations of KdV Wavetrains'', Physica D **3**, 335-343 (1981).

25.
"Shock Waves in
the Toda Lattice: Analysis'' (with B. J. Holian and
H. Flaschka), Phys. Rev. A **24**, 2595-2623
(1981).

26.
"Nonlinear **45**,
157-209 (1982).

27.
"Spectral Theory
of the Periodic Sine-Gordon Equation: A Concrete Viewpoint'' (with **23**,
1248-1277 (1982).

28.
"Breather
Annihilation by Simple Dissipation'' (with E. A. Overman),
Phys. Rev. A. **26**, 3497-3507 (1982).

29.
"Modulations of
Sine-Gordon and Sine-Gordon Wavetrains'' (with **68**, 11-59 (1983).

30.
"Solitary Waves
as Fixed Points of Infinite Dimensional Maps in an Optical Bistable
Ring Cavity'' (with J. V. Moloney and A. C. Newell),
Phys. Rev. Lett. **51**, 75-78 (1983).

31.
"Modulational Stability of Two Phase Sine Gordon Wavetrains'' (with **71**, 91-101 (1984).

32.
"Modulations of
Perturbed KdV Wavetrains''
(with **44**, 287-300 (1984).

33.
"Interactions Between Mean Flow and Finite-Amplitude Mesoscale
Eddies in a **29**, 333-353 (1984).

34.
"Chaos and
Nonlinear Modes in a Perturbed Toda Chain'' (with A. Bishop, K. Fesser, and B. Holian), Phys.
Rev. A. **31**, 2728-2731 (1985).

35.
"New Class of
Instabilities in Passive Optive Cavities'' (with J.
V. Moloney and A. C. Newell), Phys. Rev. Lett. **54**, 681-684 (1985).

36.
"Convection of
Microstructure and Related Problems'' (with G. Papanicolaou
and O. Pironneau), **45**, 780-797 (1985).

37.
"The Origin and
Saturation of Modulational Instabilities'' (with **18**, 472-474 (1986).

38.
"Focusing
Singularity of the Cubic Schrödinger Equation'' (with P. Sulem,
C. Sulem and G. Papanicolaou),
Phys. Rev. A. **34**, 2, 1200-1210 (1986).

39.
"Chaos and
Coherent Structures in pde's (with A. Aceves, H. Adachihara, C. Jones,
J. C. Lerman, J. V. Moloney
and A. C. Newell), Physica D **18**, 85-112
(1986).

40.
"Coherence and
Chaos in the Driven Damped Sine-Gordon Equation: Measurement of the Soliton Spectrum'' (with A. R. Bishop and E. A. Overman), Physica D **19**,
1-41 (1986).

41.
"Oscillations and
Instabilities in Near Integrable pde's''
(with **23**,
3-46 (1986).

42.
"Modulational Instabilities of Periodic Sine-Gordon Waves: A
Geometric Analysis'' (with **23**,
149-166 (1986).

43.
"A Quasi-Periodic
Route to Chaos in a Near-Integrable pde'' (with A. R. Bishop,

44.
"Phase-Pulling
and Space-Time Complexity in an AC Driven Damped One-Dimensional Sine-Gordon
System'' (with A. Mazor and A. Bishop), Phys. Lett. A. **119** No. 6, 273-279 (1986).

45.
"On the
Construction of a Modulating Multiphase Wavetrain for
a Perturbed KdV Equation'', IMA. **2**, 167-195
(1986).

46.
"On the Weak
Limit of Rapidly Oscillating Waves'' (with L. Chierchia,
**55**, 759-764 (1987).

47.
"Solitary Waves
as Fixed Points of Infinite-Dimensional Maps for an Optical Bistable
Ring Cavity: Analysis'' (with J. Adachihara, J. Moloney, and A. C. Newell), J. Math. Phys. **29**, 63-85
(1988).

48.
"Hamiltonian
Structure for the Modulation Equations of a Sine-Gordon Wavetrain''
(with **55**, 949-983 (1988).

49.
"Quasi-Periodic
Route to Chaos in a Near-Integrable pde: Homoclinic Crossings''(with A. Bishop, **126**, 335-340 (1988).

50.
"Geometry of the Modulational Instability:

51.
"Global
Co-ordinates for the Breather-Kink (Antikink)
Sine-Gordon Phase Space: An Explicit Separatrix as a
Possible Source of Chaos'' (with M. Salerno and A. Bishop), Phys. Rev. A **40**,
6463-6469 (1989).

52.
"Geometry of the Modulational Instability: Part III. Homoclinic
Orbits for the Periodic sine-Gordon Equation'' (with **43**, 348-384 (1990).

53.
"Stability and
Bifurcation of Spatially Coherent Solutions of the Damped-Driven NLS
Equations'' (with E. Overman, G. Terrones
and A. J. Pearlstein), **50**, 791-818 (1990).

54.
"A Modal
Representation of Chaotic Attractors for the Driven, Damped Pendulum Chain''
(with A. R. Bishop, **29**, 17-25 (1990).

55.
"Correlations Between Chaos in a Perturbed Sine-Gordon Equation and a
Truncated Model System'' (with A. R. Bishop, R. Flesch,
**21**, 1511-1536 (1990).

56.
"Toward a
Topological Classification of Integrable pde's'' (with

57.
"Some Notes on
Beltrami Fields in Cartesian Geometry'' (with O. Pironneau),
J. Math. Phys. **32**, 797-804 (1991).

58.
"Notes on Melnikov Integrals for Models of the Driven Pendulum
Chain'' (with

59.
"Chaotic and Homoclinic Behavior for Numerical Discretization
of Nonlinear Schrödinger'' (with C. Schober), Physica D **57**, 447-465 (1992).

60.
"Whiskered Tori for the NLS Equation'', Solitons
in the 80's eds. by T. Fokas and V. Zakharov, (1992).

61.
"Attractors and
Transients for a Perturbed Periodic KdV Equation: A
Nonlinear Spectral Analysis'' (with **3**,
477-539 (1993).

62.
"Strongly
Nonlinear Modal Equations for Nearly Integrable PDEs'' (with **3**, 393-426
(1993).

63.
"Filamentation and Undulation of Self-Focused Laser Beams in
Liquid Crystals'' (with E. Braun, L. R. Faucheux, A. Libchaber, D. Muraki and M.
Shelley), Europhys. Lett. **23**
(4), 239-244 (1993).

64.
"Light
Interacting with Liquid Crystals'' (with D. Muraki
and M. Shelley), Physica D **168**, 116-126
(1993).

65.
"Whiskered Tori for Integrable pde's: Chaotic Behavior in Near Integrable
pde's'' (with E. Overman),
Surveys in Appl. Math **1**, 83-200 (1994).

66.
"Semi-Classical
Behavior in the NLS Equation: Optical Shocks-Focusing Instabilities'' (with J. Bronski), Proc. Lyon Conf. on Dispersive Regularization, **320**,
21-38 (1994).

67.
"The Behavior of
Solutions of NLS Equation in the Semiclassical
Limit'' (with S. Jin and D. Levermore), Proc. **320**,
235-255 (1994).

68.
"Computing the
Weak Limit of KdV'' (with J. Strain), to have
appeared, Proc. Lyon Conf. on Dispersive Regularization, (1994), (did not
appear due to editor's error).

69.
"Calculating the
Weak Limit of KdV'' (with J. Strain), Comm. Pure Appl. Math. **XLVII**, 1-46 (1994).

70.
"Morse and Melnikov Functions for NLS pde's''
(with Y. Li), Comm. Math. Phys. **162**, 175-214 (1994).

71.
"A Paraxial Model
for Optical Self-Focusing in a Nematic Liquid
Crystal'' (with D. Muraki, M. Shelley and X. Wang), Physica D **26**, 55-81 (1995).

72.
"Whiskered Tori and Chaotic Behavior in Nonlinear Waves,'' Proceedings
of International Congress of Mathematicians, Zürich, 1484-1493 (1995).

73.
"Melnikov Analysis of Numerically Induced Chaos in the
Nonlinear Schrödinger Equation'' (with A. Calini, N.
M. Ercolani and C. M. Schober),
Physica D, **89**, 227-260 (1995).

74.
"Persistent Homoclinic Orbits for a Perturbed Nonlinear Schroedinger Equation'' (with Y. Li, J. Shatah
and S. Wiggins), Comm. Pure Appl. Math. **XLIX**,
1175-1255 (1996).

75.
"Self-Focused
Optical Structures in a Nematic Liquid Crystal''
(with D. Muraki and M. Shelley), Physica
D **97**, 471-97 (1996).

76.
"Homoclinic Orbits in a Four Dimensional Model of a
Perturbed NLS Equation: A Geometric Singular Perturbation Study'' (with E. Overman, S. Wiggins, and C. Xiong),
Dynamics Reported **V**, 190-287 (1996).

77.
"Melnikov Analysis for Pde's''
(with J. Shatah), Lectures in Applied Mathematics, **31**,
51-100 (1996).

78.
"On the Stability
of Time-Harmonic Localized States in a Disordered Nonlinear Medium'' (with J.
C. Bronski, M. Shelley), J. Stat. Phys. **88**,
1077-1115, (1996).

79.
"Homoclinic Orbits for Pde's, in
Recent Advances in Partial Differential Equations'' (with J. Shatah), eds. R. Spigler, ^{th} birthdays) **54** AMS, 281-299 (1998).

80.
"Homoclinic Orbits and Chaos in Discretized
Perturbed NLS Systems - **7**, 211-269 (1997).

81.
"A
One-Dimensional Model for Dispersive Wave Turbulence'' (with A. Majda and **7**, 9-44 (1997).

82.
"The Semiclassical Limit of the Defocusing NLS Hierarchy'' (with
D. Levermore and Shan Jin), Comm. Pure Appl. Math. **LII** 613-654 (1999).

83.
"Spatial-Temporal
Chaos and Effective Stochastic Dynamics for a Near Integrable
Nonlinear System'' (with D. Cai
and J. Shatah), Phys. Lett.
A **253**, 280-86 (1999).

84.
"Focusing-Defocusing
Effects for Diffusion Dominated Bistable Optical
Arrays'' (with Y. Chen), Journal of the Optical Society B **16** No. 7,
1087-1098 (1999).

85.
"Modelling of Orientation Dynamics in Visual Cortex'' (with
R. Shapley, M. Shelley and J. Wielaard), Society for
Neuroscience Abstracts **25** (1999).

86.
"Point Neuron and
Mean Firing Rate Models of an Input Layer of the Primary Visual Cortex'' (with
M. Shelley), preprint (1999).

87.
"Spectral
Bifurcations in Dispersive Wave Turbulence'' (with D. Cai, A. Majda, **96**, 14216-14221 (1999).

88.
"Diffraction
Effects on Diffusive Bistable Optical Arrays'' (with
Y. Chen), Physica D **138**, 163-195 (2000).

89.
"Non-Focusing
Instabilities in Coupled, Integrable Nonlinear
Schrödinger PDE's'' (with **10**, 291-331
(2000).

90.
"Propagation of
the Electromagnetic Field in Optical Limiting Reverse Saturable
Absorbers'' (with S. Kim and M. Potasek), Phys. Rev.
A **61**, 025801-1 - 025801-4 (2000).

91.
"A Neuronal Network
Model of the Macaque Primary Visual Cortex V1: Orientation Tuning and Dynamics
in the Input Layer 4Cα" (with R. Shapley, M. Shelley, J. Wielaard), Proc. Nat. Acad. **97**, 14, 8087-8092
(2000).

92.
"Chaotic and
Turbulent Behavior of Unstable 1-D Nonlinear Dispersive Waves'' (with D. Cai), Journal of Mathematical
Physics, **41**, 6, 4125-4153 (2000).

93.
"All
Optical-Power Limiting''(with M. Potasek
and S. Kim), J. Nonlinear Physics and Materials, **9**, 343-364 (2000).

94.
"Spatiotemporal
Chaos in Spatially Extended Systems'' (with D. Cai and J. Shatah), J.
Mathematics and Computers in Simulation 55 (4-6) 329-340 (2001).

95.
"Dispersive Wave
Turbulence In One Dimension'' (with D. Cai, A. J. Majda, **152-153** (2001) 551-572.

96.
"How Simple Cells
are Made in a Nonlinear Network Model of the Visual Cortex'' (with R. Shapley,
M. Shelley, J. Wielaard), Journal of Neural Science, **21**
(14), 5203-5211 (July 2001).

97.
"Modulations in
the Leading Edges of Midlatitude Storm Tracks'' (with
R. Goodman and A. Majda), ** 62**, 3: 746-776 (2001).

98.
"Lateral
Inhibition Generates Simple Cells in a Model of V1 Cortex'' (with R. Shapley,
M. Shelley and J. Wielaard), Inv. Ophthalmol
and Vis. Sci. **42**, (2001).

99.
"Complex Cells in
a Simple Cell Network Model of V1 Cortex'' (with R. Shapley, M. Shelley and L.
Tao), Society for Neuroscience Abstracts **27**, (2001).

100.
"The Nonlinear
Schrödinger Equation as both a PDE and a Dynamical System '' (with D. Cai and K.T.R. McLaughlin), *Handbook of Dynamical Systems, vol. 2*,
Elsevier Science B.V. 599-678 (2002).

101.
"** **States of high conductance in a large-scale
model of the visual cortex '' (with R.
Shapley, M. Shelley and J. Wielaard), Journal of Computational Neuroscience **13,** (2): 93-109 (2002)

102.
"Coarse-Grained
Reduction and Analysis of a Network Model of Cortical Response: ** **Journal
of Computational Neuroscience** 12**
(2): 97-122 (2002).

103.
"Orientation
Selectivity: models and neural mechanisms'' (with R. Shapley and M. Shelley), *The Handbook of Brain Theory and Neural
Networks, Second Edition*, MIT Press (2002).

104.
"High Conductance
Dynamics of the Primary Visual Cortex. (with R. Shapley, M. Shelley, and J.
Jin), Perspectives and Problems in Nonlinear Science: A celebratory volume in
honor of Lawrence Sirovich, Springer-Verlag New York, Inc. (2003)

105.
"Large-scale
modeling of the primary visual cortex: influence of cortical architecture upon
neuronal response" (with R. Shapley and M. Shelley), Journal of Physiology
. Paris **97** 237-252 (2003).

106.
"An egalitarian network model for the
emergence of simple and complex cells in visual cortex" (with L. Tao, M.
Shelley and R. Shapley) PNAS **101**
(1): 366-371 (2004).

107.
"An effective kinetic representation of
fluctuation-driven neuronal networks with application to simple and complex
cells in visual cortex" (with D. Cai, L. Tao , M. Shelley) PNAS **101** (20): 7757-7762 (2004).

108.
"An Embedded Network Approach for Scale-Up
of Fluctuation-Driven Systems with Preservation of Spike Information"
(with D. Cai, L. Tao ) PNAS **101**
(39): 14288-14293 (2004).

109.
"Architectural and synaptic mechanisms underlying
coherent spontaneous activity in V1" (with D. Cai,
A. Rangan
) PNAS **102** (16): 5868- 5873 (2005).

110.
"Modeling the spatiotemporal cortical activity
associated with the line-motion illusion in primary visual cortex" (with
A. Rangan, D. Cai) PNAS **102**
(52): 18793-18800 (2005).

111.
"Kinetic Theory for Neuronal Network
Dynamics" (with D. Cai,
L. Tao, A. Rangan) Comm. Math. Sci
**4** (1): 97-127 (2006).

112.
"Orientation Selectivity in Visual Cortex by
Fluctuation-Controlled Criticality" (with L. Tao, D. Cai, M. Shelley, and R. Shapley) PNAS **103** (34): 12911-12916 (2006).

113.
"Estimation of Synaptic Conductances"
(with A. Guillamon and J. Rinsel)
J. Physiology-
**100** ( 1-3): 31-42 (2006).

114.
"Neuronal Information Encoding and Reduction of Dimension Network Dynamics" (with D. Cai, A. Rangan) SIAM **40** (2) (2007).

115.
"Quantifying Neuronal Network Dynamics through Coarse-Grained Event-Trees" (with A. Rangan, D. Cai) PNAS, **105** (2008), no. 31, 10990-10995.

116.
"The Role of Fluctuations in Coarse-Grained Descriptions of Neuronal Networks" (with D. Cai, L. Tao, M. Shkarayev, A. Rangan, G. Kovacic) Comm. Math. Sci, **10** (2012), no. 1, 307-354.

117.
"Spatiotemporal Dynamics of Neuronal Population Response in the Primary Visual Cortex" (with D. Zhou, A. Rangan, D. McLaughlin, D. Cai) PNAS, **110** (2013), no. 23 9517-9522.

**BOOKS (EDITED)**

1.
"Theory and
Applications of Solitons'' (ed. with H. Flaschka), Proc. of NSF Conf. on Solitons,
Special Volume of the Rocky Mountain Math. Journal (1978).

2.
"Inverse
Problems'' (ed.), Proc. of AMS-SIAM Conf. 1983.

7/29/08