Section: New Results
Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve
The preprint [58] is devoted to the cubic nonlinear Schrödinger equation in a two dimensional waveguide with shrinking cross section of order . For a Cauchy data living essentially on the first mode of the transverse Laplacian, we provide a tensorial approximation of the solution in the limit , with an estimate of the approximation error, and derive a limiting nonlinear Schrödinger equation in dimension one with an additional effective potential depending on the curvature.