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We consider a scalar Fermi–Pasta–Ulam (FPU) system on a square 2D lattice. The Kadomtsev–Petviashvili (KP-II) equation can be derived by means of multiple scale expansions to describe unidirectional long waves of small amplitude with slowly varying transverse modulations. We show that the KP-II approximation makes correct predictions about the dynamics of the original scalar FPU system. An existing approximation result is extended to an arbitrary direction of wave propagation. The main noveltydoi:10.5445/ir/1000151189 fatcat:umba6phctfaype2u6xarjy47iu