Toda lattice solutions converge globally in time to KdV solutions in the long-wave continuum limit.
Schneider,Bounds for the nonlinear Schr¨ odinger approximation of the Fermi-Pasta-Ulam system.Appl
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The Korteweg-de Vries limit for the global dynamics of the Toda lattice
Toda lattice solutions converge globally in time to KdV solutions in the long-wave continuum limit.