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International audienceThis paper is devoted to the cubic nonlinear Schrödinger equation in a two dimensional waveguide with shrinking cross section. For a Cauchy data living essentially on the first mode of the transverse Laplacian, we provide a tensorial approximation of the solution in this limit, with an estimate of the approximation error, and derive a limiting nonlinear Schrödinger equation in dimension one

Strong Confinement Limit for the Nonlinear Schrödinger Equation Constrained on a Curve