Infinitely-Precise Space-Time Discretizations of the Equation ut + uux = 0

  • B. A. Kupershmidt
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 26)


The classical Volterra system u n,t = constu n (u n+i u n−i ) is time-discretized in four different ways such that each one of the infinity of conservation laws of the Volterra system is preserved exactly. Since in the space-continuous limit the Volterra system turns into the basic nonlinear infinite-dimensional dynamical system u t + uu x = 0, the Volterra conservation laws are discretizations of the conservation laws (u m /m) t + [(u m+1/(m+1)] x = 0, mN.


Toda Lattice Volterra System Toda Theory Inviscid Burger Equation Typical Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Suris, Yu. B., Leningrad Math. J. 2 (1991), 339.MathSciNetMATHGoogle Scholar
  2. [2]
    Suris, Yu. B., Phys. Lett. A 145 (1990), 113.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Gibbons, J. and Kupershmidt, B. A., Phys. Lett. A 165 (1992), 105.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Veselov, A. R, Punct. Anal. Appl. 22 (2) (1988), 1; 25 (2) (1991), 38.Google Scholar
  5. [5]
    Moser, J. and Veselov, A. R, Comm. Math. Phys. 139 (1991), 217.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Veselov, A. P., Uspekhi Mat. Nauk 46 (5) (1991), 3.MathSciNetMATHGoogle Scholar
  7. [7]
    Kupershmidt, B. A., Discrete Lax Equations and Differential-Difference Calculus, Asterisque, Paris (1985).Google Scholar

Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • B. A. Kupershmidt
    • 1
  1. 1.The University of Tennessee Space InstituteTullahomaUSA

Personalised recommendations