Abstract:We prove that the solutions to the discrete Nonlinear Schrödinger Equation (DNLSE) with nonlocal algebraically-decaying coupling converge strongly in L 2 (R 2 ) to those of the continuum fractional Nonlinear Schrödinger Equation (FNLSE), as the discretization parameter tends to zero. The proof relies on sharp dispersive estimates that yield Strichartz estimates that are uniform in the discretization parameter. An explicit computation of the leading term of the oscillatory integral asymptotics is used to show t… Show more
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