Work

Dynamics near the origin of the long range scattering for the one-dimensional Schrödinger equation

Year: 2024

Type: article

Abstract: We consider the cubic Schrödinger equation on the line, for which the scattering theory requires modifications due to long range effects. We revisit the construction of the modified wave operator, and recall the construction of its inverse, in order to describe the asymptotic behavior of these operators near the origin. At leading order, these operators, whose definition includes a nonlinear modification in the phase compared to the linear dynamics, correspond to the identity. We compute explicitly the first corrector in the asymptotic expansion, and justify this expansion by error estimates.

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.676

Author: Rémi Carles

Institutions: Centre National de la Recherche Scientifique, Institut de recherche mathématique de Rennes, Université de Rennes

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Centre Henri Lebesgue, Agence Nationale de la Recherche

Awards: Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation, G5539822453