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)

Abstract

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.

Keywords

haCI 

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Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

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

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