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, m ∈ N.
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In Memory of Irene Dorfman
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© 1997 Birkhäuser Boston
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Kupershmidt, B.A. (1997). Infinitely-Precise Space-Time Discretizations of the Equation ut + uux = 0. In: Fokas, A.S., Gelfand, I.M. (eds) Algebraic Aspects of Integrable Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 26. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2434-1_10
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DOI: https://doi.org/10.1007/978-1-4612-2434-1_10
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7535-0
Online ISBN: 978-1-4612-2434-1
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