Dynamics near the origin of the long range scattering for the one-dimensional Schrodinger equation
arxiv(2024)
摘要
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.
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