Computation and Innovation in the Nonlinear Sciences

  • Norman J. Zabusky
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 75)


As the lead-off speaker I would like to reflect on the previous School of Nonlinear Mathematics and Physics [Zabusky, 1968] that Martin Kruskal and I organized 14 years ago. Several members of the present faculty or their teachers were there. W. Heisenberg, well-known for his pioneering contributions to quantum mechanics, opened the School with a talk “Nonlinear Problems in Physics” [Heisenberg, 1967] that I take the liberty of distilling into four aphorisms:
  1. 1.

    Simplification by symmetrizing.

  2. 2.

    Initial progress by linearizing.

  3. 3.

    General features by statistical methods.

  4. 4.

    Apparently coherent phenomena with long-time unpredictability.



Nonlinear Problem Present Faculty Partial Differential Equa Graphical Output Nonlinear Science 
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  1. Heisenberg, W., 1967, Nonlinear problems in physics, Physics Today, May issue, p. 27. Also published [Zabusky, 1968 ]Google Scholar
  2. Jung, C.J., and Pauli, W., 1955, “The Interpretation of Nature and the Psyche,” Bollingen Series LI, Pantheon Books.Google Scholar
  3. Taub, A., (ed.), 1963, “Collected Work of John von Neumann,” Vol. 5, McMillan, New York.Google Scholar
  4. Zabusky, N.J., ed., 1968, “Topics in Nonlinear Physics,” Sections by W. Heisenberg, C. Truesdell, I. Prigogine, M. Baus, N. Bloembergen, P.G. Saffman and J.A. Wheeler, Springer-Verlag, New York.MATHGoogle Scholar
  5. Zabusky, N.J., 1981, Computational synergetics and mathematical innovation, J. Comp. Phys., to be published.Google Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • Norman J. Zabusky
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of PittsburghPittsburghUSA

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