Infinitely-Precise Space-Time Discretizations of the Equation ut + uux = 0
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, m ∈ N.
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