Selected publications of Gadi Fibich

 

Book: THE NONLINEAR SCHRODINGER EQUATION, Springer 2015

 

 

 

 

 Nonlinear Optics/theory

       

       

Nonlinear Optics/theory/Stability of solitons        

 

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 





    
    

Nonlinear Optics/theory/Collapsing (singular) solutions

 

 Loss of phase and universality of stochastic interactions between laser beams  
Optics Express 25: 24387-24399, 2017

 

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
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

 

 

Nonlinear Optics/theory/The Biharmonic NLS (fourth-order dispersion) 

 

            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

 

 

 

 

 

Nonlinear Optics/numerical methods

         

Nonlinear Optics/numerical methods/Nonlinear Helmholtz equation

              

           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


             

Nonlinear Optics/numerical methods/Nonlinear Schrödinger equation

 

          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

 

 

 

 


 

 

 

    

Nonlinear Optics/experiments

 

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

 

Perturbations Theory

 

             Averaging principle for second-order approximation of heterogeneous models with homogeneous models   

              Proceedings of the National Academy of Sciences 109: 19545-19550, 2012

              Supplementary material  

    

Auctions

 

Revenue equivalence of large asymmetric auctions
Available at SSRN

 

             Large asymmetric first-price auctions --- a boundary-layer approach
         
  SIAM Journal on Applied Math 75, 229-251, 2015

            supplementary material

 

            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

 

      

 

Marketing

 

Marketing/diffusion of new products

 

 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

 

The diffusion of legal innovation – a mathematical modeling approach
 
Available at SSRN

 

 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

  Online supplement

Marketing/nonlinear pricing

 

            Optimal three-part tariff plans
            Operations Research 65:1177-1189, 2017

            Supplementary Material

 

         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

 

 

             Law

 

The diffusion of legal innovation – a mathematical modeling approach
 
Available at SSRN

 

Numerical Linear Algebra

 

          Efficient solution of Ax(k) = b(k) using A-1
           Journal of Scientific Computing  32: 29-44, 2007


Biochemistry

 

          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

 

 

 

Lasers in Medicine

 

 

 

Coronary Blood flow

 

          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

 

 

 

 

 

    

Queueing Theory

 

          A Communication Multiplexer Problem: Two Alternating Queues with Dependent Randomly-Timed Gated Regime
           Queueing Systems 42: 325-353, 2002

 

 

   Computer Graphics

 

  •  B. Nadler, G. Fibich, S. Lev-Yehudi and D. Cohen-Or

          A qualitative and quantitative visibility analysis in urban scenes
           Computers & Graphics 23: 655-666, 1999

 

  •  D. Cohen-Or, G. Fibich, D. Halperin and E. Zadicario

          Conservative visibility and strong occlusion for viewspace partitioning of densely occluded scenes
           Computer Graphics Forum 17: 243-253, 1998


 

 

 

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