Leading order integrability conditions for differential-difference equations

Abstract A necessary condition for the existence of conserved densities, ρ, and fluxes of a differential-difference equation which depend on q shifts, for q sufficiently large, is presented. This condition depends on the eigenvalues of the leading terms in the differential-difference equation. It also gives, explicitly, the leading integrability conditions on the density in terms of second derivatives of ρ.

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