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We present a discrete multiscale expansion of the lattice potential Korteweg-de Vries (lpKdV) equation on functions of an infinite order of slow varyness. To do so, we introduce a formal expansion of the shift operator on many lattices holding at all orders. The lowest secularity condition from the expansion of the lpKdV equation gives a nonlinear lattice equation, depending on shifts of all orders, of the form of the nonlinear Schrodinger equation

Multiscale expansion of the lattice potential KdV equation on functions of an infinite slow-varyness order