Book: THE NONLINEAR SCHRODINGER
EQUATION, Springer 2015
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Explicit solutions of the Bass and SI
models on hypernetworks
ArXix 2407.12123
Monotone convergence of spreading
processes on networks
ArXix 2407.10816
Boundary effects in the diffusion of new
products on Cartesian networks
Operations Research - accepted
Universal
bounds for spreading on networks
Chaos 34: 053101, 2024
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