Dynamics near the origin of the long range scattering for the one-dimensional Schrodinger equation
arXiv:2402.06400 · doi:10.5802/crmath.676
Abstract
We consider the cubic Schrodinger 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.
A flaw was fixed in Lemma 2.2 More explanations and references
References in corpus (4)
- Scattering and small data completeness for the critical nonlinear Schroediger equation
- Modified scattering for the critical nonlinear Schrödinger equation
- Analyticity of the scattering operator for semilinear dispersive equations
- Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions