BINARY MODULATED OSCILLATIONS IN A SEMIDISCRETE VERSION OF BURGERS-EQUATION

In this paper we study, both analytically and numerically, the binary modulated oscillations which arise in an integrable, semi-discrete app roximation to inviscid Burgers. Explicit solutions of the binary modul ation equations, derived in Goodman and Lax (1988), are found for seve ral choices of initial data. Observations, based on numerical experime nts, are presented as to which initial data lead to solutions containi ng purely binary oscillations. Comparisons are made to the integrable theory of the Kac-van Moerbeke and Toda lattices. Non-integrable schem es, for which the binary oscillations also remain hyperbolic, are pres ented, and explicit solutions of their binary modulation equations are found.