Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve

Florian Méhats (1) , Nicolas Raymond (2)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes

This 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.

Domaines: Mathématiques [math]

Florian Méhats, Nicolas Raymond. Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve. Annales Henri Poincaré, 2017, 18 (1), pp.281-306. ⟨10.1007/s00023-016-0511-8⟩. ⟨hal-01090045⟩