Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve - Archive ouverte HAL
Article Dans Une Revue Annales Henri Poincaré Année : 2017

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

Résumé

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.
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Dates et versions

hal-01090045 , version 1 (02-12-2014)

Identifiants

Citer

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⟩
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