Book: THE NONLINEAR SCHRODINGER
EQUATION, Springer 2015
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Funnel theorems for spreading on
networks
ArXiv 2308.13034
Compartmental
limit of discrete
Bass models on networks
Discrete and Continuous Dynamical
Systems 28: 3052-3078, 2023
Diffusion
of new products with heterogeneous consumers
Mathematics of Operations Research
48: 257-287, 2023
Exact
description of SIR-Bass epidemics on 1D lattices
Discrete and Continuous Dynamical
Systems 42, 505-535, 2022
Percolation
of new products
Physica
A 540: 123055, 2020
The diffusion of legal innovation – insights from mathematical
modeling
Cornell International Law Journal 52:
313-349, 2019
Boundary
effects in the discrete Bass model
SIAM Journal on Applied Math 79: 914-937, 2019
Diffusion
of new products with recovering consumers
SIAM Journal on Applied Math 77:
1230-1247, 2017
Bass-SIR
model for diffusion of new products in social networks
Physical Review E 94: 032305, 2016
A comparison of stochastic cellular automata diffusion with the
Bass diffusion model
Available at SSRN
Aggregate diffusion
dynamics in agent-based models with a spatial structure
Operations Research 58:
1450-1468, 2010
Optimal
three-part tariff plans
Operations Research 65:1177-1189, 2017
Optimal
price promotions in the presence of asymmetric reference-price effects
Managerial and Decisions
Economics 28: 569–577, 2007
The
dynamics of price elasticity of demand in the presence of reference-price
effects
Journal of the Academy of
Marketing Science 33: 66-78, 2005
Explicit
solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects
Operations Research 51:
721-734, 2003
paper won the 2002 Oded
Levin bi-annual prize of the Operations Research Society of Israel
Revenue
equivalence of large asymmetric auctions
SIAM Journal on Applied Math 78, 1489-1510, 2018
Large
asymmetric first-price auctions --- a boundary-layer
approach
SIAM Journal on Applied Math 75,
229-251, 2015
An
elementary proof of the common maximal bid in asymmetric first-price and all-pay auctions
Economics Letters 109,
190-191, 2014
Asymmetric
first-price auctions: A dynamical systems approach
Mathematics of
Operations Research 37: 219- 243, 2012
Numerical
simulations of asymmetric first-price auctions
Games and Economic Behavior 72,
479-495, 2011
MATLAB
CODES available here
Asymptotic
revenue equivalence of asymmetric auctions with interdependent values
European Journal of Operational Research 206: 496-507, 2010
Large
auctions with risk-averse buyers
International Journal of Game Theory 39:
359-390, 2009
All-pay auctions with risk-averse buyers
International Journal of Game Theory 34:
583-599, 2006
Revenue
equivalence in asymmetric auctions
Journal of Economic Theory 115:
309-321, 2004
Asymmetric
first-price auctions - a perturbation approach
Mathematics of Operations Research 28:
836-852, 2003
Low
and high types in asymmetric first-price auctions
Economics Letters 75: 283-287, 2002
Loss of physical reversibility in
reversible systems
Physica D 410: 132515, 2020
Loss of phase and universality of
stochastic interactions between laser beams
Optics Express 25: 24387-24399, 2017
Positive
and necklace solitary waves on bounded domains
Physica D 315: 13-32, 2016
A quantitative
approach to soliton instability
Optics Letters 36: 397-399, 2011
Simulations
of the nonlinear Helmholtz equation: Arrest of beam collapse, nonparaxial solitons and counter-propagating beams
Optics Express 16: 13323-13329, 2008
Instability
of bound states of a nonlinear Schrödinger equation with a dirac
potential
Physica D 237: 1103-1128, 2008
Analytic
theory of narrow lattice solitons
Nonlinearity 21: 509-536,
2008
Optical
light bullets in a pure Kerr medium
Optics Letters 29: 887-889, 2004
Stability of
solitary waves for nonlinear Schrödinger equations with inhomogeneous
nonlinearities
Physica D 175: 96-108, 2003
Self focusing on bounded domains
Physica D 155: 132-158, 2001
Loss
of polarization of elliptically polarized collapsing beams
Physical Review A 99: 003824, 2019
Nonlinear-damping
continuation of the nonlinear Schrödinger equation- a numerical study
Physica D 241: 519-527, 2012
Continuations
of the nonlinear Schrödinger equation beyond the singularity
Nonlinearity 24: 2003-2045, 2011
Singular
solutions of the subcritical nonlinear Schrödinger equation
Physica D 240: 1119–1122, 2011
Singular
standing-ring solutions of nonlinear partial differential equations
Physica D 239: 1968-1983, 2010
Predicting
the filamentation of high-power beams and pulses
without numerical integration: A nonlinear Geometrical Optics method
Physical Review A 78: 043807, 2008
Simulations
of the nonlinear Helmholtz equation: Arrest of beam collapse, nonparaxial solitons and counter-propagating beams
Optics Express 16:
13323-13329, 2008
Singular
ring solutions of critical and supercritical nonlinear Schrödinger equations
Physica D 231: 55-86, 2007
Paper
selected as one of the winners of the 2007 SIAM Student
Paper Competition
Proof
of a Spectral Property related to the singularity formation for the
L2 critical nonlinear Schrödinger equation
Physica D 220: 1-13, 2006
Control of
the collapse distance in atmospheric propagation
Optics Express 14: 4946-4957, 2006
Collapse
dynamics of super-Gaussian Beams
Optics Express 14: 5468-5475, 2006
New
singular solutions of the nonlinear Schrödinger equation
Physica D 211: 193-220, 2005
Self-focusing
distance of very high power laser pulses
Optics Express 13: 5897-5903, 2005
Numerical
simulations of self focusing of ultrafast laser
pulses
Physical Review E 67, 056603, 2003
Self-focusing
of circularly polarized beams
Physical Review E 67, 036622, 2003
Backscattering
and nonparaxiality arrest collapse of nonlinear waves
SIAM Journal on Applied Math 63: 1718-1736, 2003
Multiple
filamentation of circularly polarized beams
Physical Review Letters 89: 013901, 2002
Vectorial and random effects in self-focusing and in
multiple filamentation
Physica D 157: 112-146, 2001
Deterministic
vectorial effects lead to multiple filamentation
Optics Letters 26: 840-842, 2001
Self focusing on bounded domains
Physica D 155: 132-158, 2001
Self focusing in the damped nonlinear Schrödinger equation
SIAM Journal on Applied Mathematics 61: 1680-1705, 2001
Self focusing of elliptic beams: An example of the failure
of the aberrationless approximation
Journal of the Optical Society of America B 17: 1749-1758, 2000
Critical
power for self-focusing in bulk media and in hollow waveguides
Optics Letters 25: 335-337, 2000
Self-focusing
in the perturbed and unperturbed nonlinear Schrödinger equation in critical
dimension
SIAM Journal on Applied Math 60: 183-240, 1999
Self-focusing in
the complex Ginzburg-Landau limit of the critical nonlinear Schrödinger
equation
Physics Letters A 249: 286-294, 1998
A
modulation method for self-focusing in the perturbed critical nonlinear
Schrödinger equation
Physics Letters A 239: 167-173, 1998
Self-focusing
in the presence of small time dispersion and nonparaxiality
Optics Letters 22: 1379-1381, 1997
An
adiabatic law for self-focusing of optical beams
Optics Letters 21: 1735-1737, 1996
errata
Optics Letters 22: 194, 1997
Small
beam nonparaxiality arrests self-focusing of optical
beams
Physical Review Letters 76: 4356-4359, 1996
Femtosecond
laser-tissue interactions
Ophthalmic Technologies VI, Proc. SPIE 2673:93-101, 1996
Time dispersive
effects in ultrashort laser-tissue interactions
Advances in Heat and Mass Transfer in Biotechnology, HTD 322 and BTD 32:27-31,
1995
Beam
self-focusing in the presence of small normal time dispersion
Physical Review A 52: 4218-4228, 1995
Singular
solutions of the L2 supercritical biharmonic
nonlinear Schrödinger equation
Nonlinearity 24:
1843-1859, 2011 Matlab code
Ring-type
singular solutions of the biharmonic nonlinear
Schrödinger equation
Nonlinearity 23: 2867-2887, 2010
Singular
solutions of the biharmonic nonlinear Schrödinger
equation
SIAM Journal on Applied Math 70: 3319-3341, 2010
Singular
standing-ring solutions of nonlinear partial differential equations
Physica D 239:
1968-1983, 2010
Optical
light bullets in a pure Kerr medium
Optics Letters 29: 887-889, 2004
Critical
exponents and collapse of nonlinear Schrödinger equations with anisotropic fourth-order
dispersion
Nonlinearity 16: 1809-1821, 2003
Self focusing with fourth-order dispersion
SIAM Journal on Applied Math 62:1437-1462, 2002
A
High-Order Numerical Method for the Nonlinear Helmholtz Equation in
Multidimensional Layered Media
Journal of Computational Physics 228: 3789–3815, 2009
MATLAB CODES are available here
Simulations
of the nonlinear Helmholtz equation: Arrest of beam collapse, nonparaxial solitons and counter-propagating beams
Optics Express 16: 13323-13329, 2008
High-order
numerical method for the nonlinear Helmholtz equation with material
discontinuities in one space dimension
Journal of Computational Physics 227: 820-850, 2007
Fourth order
schemes for time-harmonic wave equations with discontinuous coefficients
Communications in Computational Physics 5: 442-445, 2009
High-Order
Numerical Solution of the Nonlinear Helmholtz Equation with Axial Symmetry
Journal of
Computational and Applied Mathematics 204: 477-492, 2007
Numerical
Solution of the Nonlinear Helmholtz Equation Using Nonorthogonal
Expansions
Journal of Computational.Physics
210: 183-224, 2005
Computation
of Nonlinear Backscattering Using a High-Order Numerical Method
Journal of Scientific
Computing 17: 351-364, 2002
High-order
two-way artificial boundary conditions for nonlinear wave propagation with
backscattering
Journal of Computational
Physics 171: 632-677, 2001
Numerical
simulations of self focusing of ultrafast laser
pulses
Physical Review E 67,
056603, 2003
Discretization
effects in the nonlinear Schrödinger equation
Applied Numerical
Mathematics 44: 63-75, 2003
Loss
of polarization of elliptically polarized collapsing beams
Physical Review A 99: 003824, 2019
Loss
of phase of collapsing beams
Physical Review Letters 108: 043902, 2012
Measuring
the stability of polarization orientation in high intensity laser filaments in
air
Appl. Phys. Lett. 101: 201105, 2012
Pulse-splitting
in the anomalous group-velocity-dispersion regime
Optics Express 19:
9309-9314, 2011
Control
of the filamentation distance and pattern in
long-range atmospheric propagation
Optics Express 15: 2779-2784, 2007
Control of
the collapse distance in atmospheric propagation
Optics Express 14:
4946-4957, 2006
Collapse
dynamics of super-Gaussian Beams
Optics Express 14: 5468-5475, 2006
Collapse
of Optical Vortices
Physical Review Letters 96: 133901,
2006
Self-focusing
distance of very high power laser pulses
Optics Express 13: 5897-5903, 2005
Control of
Multiple Filamentation in Air
Optics Letters 29: 1772-1774, 2004
Multiple filamentation induced by input-beam ellipticity
Optics Letters 29:
1126-1128, 2004
Self-similar
optical wave collapse: Observation of the Townes profile
Physical Review Letters 90: 203902,
2003
Averaging principle for second-order approximation of heterogeneous models with homogeneous models
Proceedings of the National Academy of Sciences 109: 19545-19550,
2012
Density estimation in uncertainty propagation
problems using a surrogate model
SIAM/ASA
Journal on Uncertainty Quantification 8: 261-300, 2020
Efficient
solution of Ax(k) = b(k) using A-1
Journal of
Scientific Computing 32: 29-44, 2007
Systematic
search for the rate constants that control the exocytotic
process by a Genetic Algorithm
Biochimica et Biophysica Acta 1763: 345-355, 2006
Determination of
a unique solution to parallel proton transfer reactions using the genetic
algorithm
Biophysical
Journal 87: 47-57, 2004
Mathematical
model of blood flow in a coronary capillary
American Journal
of Physiology 265: H1829-1840, 1993
Modeling of Coronary Capillary Flow
Advances in Experimental
Medicine and Biology 346: 137-150, 1993
A
Communication Multiplexer Problem: Two Alternating Queues with Dependent
Randomly-Timed Gated Regime
Queueing Systems 42:
325-353, 2002
A qualitative
and quantitative visibility analysis in urban scenes
Computers &
Graphics 23: 655-666, 1999
Conservative
visibility and strong occlusion for viewspace
partitioning of densely occluded scenes
Computer Graphics
Forum 17: 243-253, 1998