Henrik Kalisch

Professor of Applied Mathematics

Address:  

Education:  

• Ph.D. in Mathematics, University of Texas at Austin, 2001.
  
  
• M.A. in Mathematics
  University of Georgia in Athens, 1996.
  
  
• B.S. in Mathematics, Summa Cum Laude and with Highest Honors.
  University of Georgia in Athens, 1996.

Previous Appointments:  

• University of Bergen, Norway
  Associate Professor,
  Department of Mathematics, 2005 - 2008
  
  
• NTNU, Norway
  Research Fellow,
  Department of Mathematics, 2004 - 2005.
  
  
• Lund University, Sweden
  Research Fellow,
  Mathematics Center, Faculty of Science, 2002 - 2004
  
  
• McMaster University, Ontario
  Postdoctoral Fellow,
  Department of Mathematics and Statistics, 2001 - 2002.
  
  
• Los Alamos National Laboratory, New Mexico
  Intern at the Center for Nonlinear Studies (CNLS),
  Summer 2001.

Publications:  

• Gevrey regularity for a class of water-wave models,
  with Zoran Grujic,
  accepted for publication in Nonlinear Analysis: Theory, Methods & Applications
  
  
• A Boundary Value Problem for the KdV Equation: Comparison of Finite Difference and Chebyshev Methods,
  with Jan Ole Skogestad,
  accepted for publication in Mathematics and Computers in Simulation.
  
  
• Orbital Stability of Negative Solitary Waves,
  with Nguyet Nguyen,
  accepted for publication in Mathematics and Computers in Simulation.
  
  
• The Stability of Solitary Waves of Depression,
  with Nguyet Nguyen,
  to appear in Proceedings of 'New Trends in Harmonic and Complex Analysis'.
  
  
• Hamiltonian Formulation and Long Wave Models for Internal Waves,
  with Walter Craig and Philippe Guyenne,
  Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering, 2007.
  
  
• On the Rate of Convergence of a Collocation Projection of the KdV Equation,
  with Xavier Raynaud,
  Mathematical Modelling and Numerical Analysis 41 (2007) 95-110.
  
  
• Derivation and Comparison of Model Equations for Interfacial Capillary-Gravity Waves in Deep Water,
  Mathematics and Computers in Simulation 74 (2007) 168-178.
  
  
• Exponential Convergence of a Spectral Projection of the KdV Equation,
  with Magnar Bjørkavåg,
  Physics Letters A 365 (2007) 278-283.
  
  
• Global Solutions of the Derivative Schrödinger Equation in a Class of Functions Analytic in a Strip,
  with Jerry L. Bona and Zoran Grujic,
  Journal of Differential Equations 229 (2006) 186-203.
  
  
• Convergence of a Spectral Projection of the Camassa-Holm Equation,
  with Xavier Raynaud,
  Numerical Methods for Partial Differential Equations 22 (2006) 1197-1215.
  
  
• Solitary Waves of Depression,
  Journal of Computational Analysis and Applications 8 (2006) 5-24.
  
  
• Algebraic Lower Bounds for the Uniform Radius of Spatial Analyticity for the Generalized KdV Equation,
  with Jerry L. Bona and Zoran Grujic,
  Annales de l'Institut Henri Poincare, Non Linear Analysis 22 (2005) 783-797.
  
  
• Hamiltonian Long-Wave Expansions for Free Surfaces and Interfaces,
  with Walter Craig and Philippe Guyenne,
  Communications on Pure and Applied Mathematics 58 (2005) 1587-1641.
  
  
• Rapid convergence of a Galerkin projection of the KdV equation ,
  Comptes Rendus Mathematique 341 (2005) 457-460.
  
  
• Error Analysis of Spectral Projections of the Regularized Benjamin-Ono Equation,
  BIT 45 (2005) 69-89.
  
  
• Models for Interfacial Capillary-Gravity Waves in the Long-Wave Limit,
  in Proceedings of The Fifth International Symposium on Ocean Wave Measurement and Analysis, 2005.
  
  
• Numerical Study of Traveling-Wave Solutions of the Camassa-Holm equation, with Jonatan Lenells,
  Chaos, Solitons & Fractals 25 (2005), 287-298.
  
  
• Periodic Traveling Water Waves with Isobaric Streamlines,
  Journal of Nonlinear Mathematical Physics 11 (2004) 461-471.
  
  
• A Uniqueness Result for Periodic Traveling Waves in Water of Finite Depth,
  Nonlinear Analysis: Theory, Methods & Applications 58 (2004) 779-785.
  
  
• A New Model for Large Amplitude Long Internal Waves, with Walter Craig and Philippe Guyenne,
  Comptes Rendus Mecanique 332 (2004) 525-530.
  
  
• Singularity Formation in the Generalized Benjamin-Ono Equation, with Jerry L. Bona,
  Discrete and Continuous Dynamical Systems 11 (2004) 27-45.
  
  
• Stability of Solitary Waves for a Nonlinearly Dispersive Equation,
  Discrete and Continuous Dynamical Systems 10 (2004) 709-716.
  
  
• Dispersion-managed Solitons in the Limit of Large Energy, with Dmitry Pelinovsky,
  Proceedings of the Steklov Mathematical Institute (2003) S91 - S97.
  
  
• The Derivative Nonlinear Schrödinger Equation in Analytic Classes, with Zoran Grujic,
  Journal of Nonlinear Mathematical Physics Supplement to Volume 10 (2003) 62-71.
  
  
• Well-Posedness for the Korteweg-deVries Equation in Spaces of Analytic Functions, with Zoran Grujic,
  Differential and Integral Equations 15 (2002) 1325-1334.
  
  
• Models for Internal Waves in Deep Water, with Jerry L. Bona,
  Discrete and Continuous Dynamical Systems 6 (2000) 1-20.
  
  
• Solitary Waves in a Two-Fluid System that Includes Surface Tension, with Jerry L. Bona,
  Proceedings of the Fifth International Congress for Numerical and Mathematical Wave Propagation (2000) 324-328.
  
  
• Mass Transport and Surface Reaction of Immunoassey, with J. Buchanan, Z. Ding, et. al,
  Industrial Mathematics: The 1998 CRSC Workshop (SIAM, Philadelphia, 2000).
  
  
• Models for Internal Waves in Two-Fluid Systems, Doctoral Dissertation, University of Texas at Austin, 2001.

• A bound on oscillations of an unsteady undular bore,
  with Zoran Grujic, submitted.
  
  
• A Kdv-type Boussinesq system in a scale of Bourgain-type spaces: from the energy level to analytic spaces,
  with Jerry L. Bona and Zoran Grujic, submitted.
  
  
• Traveling waves for the Whitham equation,
  with Mats Ehrnström, submitted.
  
  
• Negative solitary waves for the generalized regularized long wave equation ,
  with Nguyet Nguyen, in preparation.
  
  
• Radius of Analyticity and Spectral Convergence for the Generalized KdV equation,
  with Magnar Bjørkavåg, in preparation.
  
  

Conference Talks:

• Traveling Waves for the Whitham Equation
  SIAM Conference on Nonlinear Waves and Coherent Structures, ,
  Rome, Italy, 2008.
  
  
• An Estimate on the Number of Rapid Oscillations of an Undular Bore
  AMS Sectional Meeting, ,
  Bloomington, Indiana, 2008.
  
  
• On the Rate of Convergence of a Spectral Approximation of the KdV Equation
  The Fifth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena ,
  Athens, Georgia, 2007.
  
  
• Solitary Waves of Depression
  AMS, 2006 Spring Central Sectional Meeting, Notre Dame,
  South Bend, Indiana, USA.
  
  
• The generalized KdV equation in analytic classes
  Workshop on PDE and Harmonic Analysis , Trondheim, Norway, 2005.
  
  
• Models for Interfacial Capillary-Gravity Waves in the Long-Wave Limit
  Ocean Waves Measurement and Analysis, WAVES 2005, Madrid, Spain, 2005.
  
  
• Model equations for internal waves
  The Fourth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena ,
  Athens, Georgia, 2005.
  
  
• Hamiltonian long-wave expansions for free surfaces and interfaces
  Recent Advances in Nonlinear PDEs , Oslo, Norway, 2005.
  
  
• Analyticity and Singularity Formation in the Generalized KdV Equation
  Nolineal 2004 , Toledo, Spain.
  
  
• Uniqueness results for periodic traveling waves
  Workshop on Free Surface Water Waves, The Fields Institute, Toronto, Ontario, Canada, 2004.
  
  
• The generalized KdV equation in analytic classes
  EquaDiff, Hasselt, Belgium, 2003.
  
  
• Hamiltonian long-wave expansions for free surfaces and interfaces
  The Third IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena ,
  Athens, Georgia, 2003.
  
  
• Well-posedness of the KdV equation in analytic classes
  Öresund Symposium in Partial Differential Equations, Lund, Sweden, 2002.
  
  
• Dispersion-managed solitons in limits of large energy
  Annual Meeting of the Canadian Mathematical Society, Quebec, Quebec, 2002.
  
  
• Models for internal waves in deep water
  The Second IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena ,
  Athens, Georgia, 2001.
  
  
• Blow-up solutions of the generalized Benjamin-Ono equation
  World Congress of Nonlinear Analysts 2000, Catania, Italy.
  
  
• Solitary waves in a two-fluid system that includes surface tension
  Waves2000, Santiago de Compostela, Spain.
  
  
• Some numerical results in the modeling of internal waves
  Texas PDE Conference, Spring 2000, Austin, Texas.
  
  
• Is the Benjamin equation integrable?
  Nonlinear Partial Differential Equations and Applications, June 1999, Lisbon, Portugal.
  

Classes Taught:

• Fluid Mechanics, for masters and Ph. D. students, University of Bergen, 2009.
  
  
• Partial Differential Equations, for masters and Ph. D. students, University of Bergen, 2008.
  
  
• Functional Analaysis, for masters and Ph. D. students, University of Bergen, 2008.
  
  
• Nonlinear Partial Differential Equations, for masters and Ph. D. students, University of Bergen, 2007.
  
  
• Fluid Mechanics, for masters and Ph. D. students, University of Bergen, 2007.
  
  
• Partial Differential Equations, for undergraduate students, University of Bergen, 2006.
  
  
• Fluid Mechanics, for masters students, University of Bergen, 2006.
  
  
• Fourier Analysis, for undergraduate students, University of Bergen, 2005.
  
  
• Ordinary Differential Equations, for masters students, Lund University, 2004.
  
  
• Partial Differential Equations, for Ph.D. students, Lund University, 2003.
  
  
• Mathemtical and Numerical Methods in Ecology, for Ph.D. students, Lund University, 2002.
  
  
• Numerical Methods for Differential Equations, advanced undergraduate level, McMaster University, 2002.
  
  
• Calculus for Business and Natural Sciences, McMaster University, 2001.
  
  
• Precalculus, University of Georgia, 1996.

Grants and Fellowships:

• Waves in Solids and Fluids
  Four-year grant from the Research Council of Norway.
  Project Leader: Professor Helge Holden
  Webpage: Wavemaker
  
  
• Stiftelsen Bokelunds Resestipendium, Lund University 2003.
• University Continuing Tuition Fellowship, University of Texas, 1999-2001
• Lefevre Departmental Fellowship, University of Texas, Fall 2000.
• Strahan Award for Outstanding Junior in Mathematics, 1994.

Referee Work:

• Advances in Differential Equations
• Applied Mathematical Modelling
• Arkiv för Matematik
• Computers and Mathematics with Applications
• Computer Methods and Programs in Biomedicine
• Discrete and Continuous Dynamical Systems
• Electronic Journal of Differential Equations
• European Journal of Physics
• Inverse Problems
• Journal of Optics
• Journal of Physics A
• Nonlinearity
• Physics Letters A
• Princeton University Press
• Proceedings of the AMS
• Proceedings of the Royal Society of London A

Scientific and Organizing Committees:

• Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, March 23-26, 2009

  Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, April 16-19, 2007
  
  

  New Trends in Complex and Harmonic Analysis , May 7-12, 2007
  
  

  Summer School on Multiscale Modeling and Simulation in Science , June 4-15, 2007