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A generalized Toda Lattice equation is considered. The associated linearproblem (Lax representation) is found. For simple case N=3 the $\tau$-functionHirota form is presented that allows to construct an exast solutions of theequations of the 1DGTL. The corresponding hierarchy and its relations with thenonlinear Schrodinger equation and Hersenberg ferromagnetic equation arediscussed.

On the Integrable Generalization of the 1D Toda Lattice