Three-dimensional conformally flat homogeneous Lorentzian manifolds

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We present a discrete multiscale expansion of the lattice potential Korteweg-de Vries (lpKdV) equation on functions of 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 Schr��dinger (NLS) equation

9 pages, submitted to Journ. Phys. A

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