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Dr. Boris A. Kupershmidt


Mathematics Program Chair
Professor of Mathematics
University of Tn Space Institute
Tullahoma, TN 37388-9700

Phone: (931) 393-7465
bkupersh@utsi.edu

Papers

Dr.Boris A. Kupershmidt

Education

  • Ph.D., Massachusetts Institute Technology, Cambridge, Massachusetts, 1979

Professional Experience

  • 1986 - Present, Professor of Mathematics, The University of Tennessee Space Institute
  • 1983 - 1986, Associate Professor of Mathematics, The University of Tennessee Space Institute
  • 1985 Chancellor Research Scholar Award
  • 1982 - 1983, T. H. Hildebrandt Research Assistant Professor of Mathematics, Department of Mathematics, University of Michigan, Ann Arbor, Michigan
  • 1982 -1983, Long term visiting staff member, Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico (on leave from the University of Michigan)
  • 1979 – 1981, T. H. Hildebrandt Research Assistant Professor of Mathematics, Department of Mathematics, University of Michigan, Ann Arbor, Michigan
  • 1977, Junior Scientific Researcher, Department of Physics, Moscow State Pedagogical Institute, Moscow
  • 1973 -1976 Special Mathematical Tutor, Mathematical and Physical High School #444, Moscow
  • 1971-1973 Probationer -researcher in heat and mass transfer. All Union Institute of Mechanization of Agriculture, Moscow

Courses Taught

  • Math 404 - Applied Vector Calculus
  • Math 435 - Partial Differential Equations
  • Math 443 - Complex Variables
  • Math 517 - Mathematical Methods in Physics
  • Math 518 - Mathematical Methods in Physics
  • Math 519A - Seminar in Applied Mathematics
  • Math 519 - Special Functions
  • Math 619 - Seminar in Applied Mathematics
  • Math 598 - Graduate Reading in Mathematics

Research Interests

I work in those areas of mathematical physics that deal with the dynamics of conservative systems: particles, fields, fluids, plasmas, etc., and mostly with those systems that exhibit regular behavior (the so-called "integrable systems", both classical and quantum).

Major Publications/Books

  • Discrete Lax Equations and Differential-Difference Calculus, Asterisque (Paris 1985)
  • Elements of Superintegrable Systems. Basic Technique and Results, Reidel (Dordrecht 1987)
  • The Variational Principles of Dynamics, World Scientific (Singapore 1992).
  • KP or mKP: Noncommutative Mathematics of Lagrangian, Hamiltonian, and Integrable Systems, American Mathematical Society (Providence 2000); translated into Russian by Regular and Chaotic Dynamics (Moscow-Izhevsk 2002)
  • "Integrable and Superintegrable Systems",  Boris A. Kupershmidt., ed.,  World  Scientific,  (Singapore, 1990).

Refereed Publications
Over 150 papers, the latest;

  • Kupershmidt, B.A., “Quantum Differential Forms”, J. Nonlin. Math Physics 5 Phys. 6 (1999) 448-488.
  • Kupershmidt, B.A., “q-Probability:  I. Basic Discrete Distributions”,  J. Nonlin. Math. Phys. 7 (2000) 73-93.
  • Kupershmidt, B.A., “q-Newton Binomial:  From Euler to Gauss”, J. Nonlin,  Math. Phys. 7 (2000) 136-154.
  • Kupershmidt, B.A., “.... And Free Lunch For All.   A Review of Bruce C. Berndt's Ramanujan's Notebooks, Parts I-V”,  J. Nonlin. Math. Phys. 7 (2000) (R7-R37).
  • Kupershmidt, B.A., “Dark Equations”,  J. Nonlin. Math. Phys. 8  (2001)  363-445.
  • Kupershmidt, B.A., “q-Analogs of Classical 6-Periodicity: From Euler to Chebyshev”, J. Nonlin. Math. Phys. 10 (2003), 318-399.
  • Kupershmidt, B.A., “On A Group of Automorphisms of the Noncommutative Burgers Hierarchy,” J. Nonlin. Math Phys. 12 (2005) 549-559.
  • Kupershmidt, B.A., “Reflection  Symmetries of q-Bernoulli Polynomials,” J. Nonlin. Math. Phys. 12 Suppl. 1 (2005) 412-422.
  • Kupershmidt, B.A., “Extensions of 1-Dimensional Polytropic Gas Dynamics,” J. Nonlin. Math. Phys. 13 (2006), 145-157.
  • Kupershmidt, B.A., “Extended Equations of Long Waves,” Studies in Appl. Math. 116 (2006) 415-434.
  • Kupershmidt, B.A., “Equations of Long Waves With A Free Surface III.  The Multidimensional Case,” J. Nonlin. Math. Phys. 12 (2005) 508 / 517.
  • Kupershmidt, B.A., “Left-Symmetric Algebras in Hydrodynamics,” Lett. Math. Phys. (To appear).
  • Kupershmidt, B.A., “Noncommutative Integrable Systems of Hydrodynamic Type,” Acta Appl. Math. (To appear).
  • Kupershmidt, B.A., “Equations of Long Waves With a Free Surface IV.  The Case of Constant Shear,” (submitted to Physics D).
  • Kupershmidt, B.A., “Hydrodynamical Chains of Pavlov Class,” (to appear in Physics Letters A.).
  • Kupershmidt, B.A., “Integrability of 1 Jet of a Class Noncommutative Hydrodynamic Chains,” (to appear in Korean Math. J.; invited paper).
  • Kupershmidt, B.A., “A Deformation of Lax Pseueodifferential Operators,  Skewsymmetric and General,” (to appear in Russian Math. J.; invited paper).

Presentations at National/International Meetings

  • 1991, USA - USSR Workshop on "Nonlinear Physics", Potsdam, NY.
  • 1992, International Conference on "Dynamical Systems", Cincinnati, Ohio.
  • 1996, International Workshop on Special Functions. Montreal, CA
  • 1999, XXXI International Symposium on Mathematical Physics, Nicholas Copernicus University, Poland
  • 2001, 971st Meeting of the American Mathematical Society, Williams College, MA, USA

Proposal Awarded

  • "New Directions in Integrable Systems", awarded by the National Science Foundation (NSF), 1993 - 1995.