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A hierarchy of differential-difference equations, conservation laws and new integrable coupling system. (English) Zbl 1222.37077

Summary: Starting from a discrete spectral problem with two arbitrary parameters, a hierarchy of nonlinear differential-difference equations is derived. The new hierarchy not only includes the original hierarchy, but also the well-known Toda equation and the relativistic Toda equation. Moreover, infinitely many conservation laws for a representative discrete equation are given. Further, a new integrable coupling system of the resulting hierarchy is constructed.

MSC:

37K60 Lattice dynamics; integrable lattice equations
39A70 Difference operators
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