Friday, June 21, 2019 - 14:15 in D5-153
Failure of scattering with localized waves for nonlinear Schrodinger equations with long-range interaction
A talk in the Oberseminar Analysis series by
Kenji Nakanishi
| Abstract: |
This is joint work with Jason Murphy. We consider asymptotic
behavior of solutions for large time to the nonlinear Schrodinger
equation with power or Hartree nonlinearity. It is well known that the
nonlinear solutions can not be approximated by free ones in L2, if the
nonlinear interaction decays too slow for small amplitude or in
spatial distance, namely in the long-range case. We extend it to the
case where the solution is decomposed for large time into a localized
part and a dispersive part, as is expected in the soliton resolution
conjecture. More precisely, we prove that the dispersive part can not
be a free solution, under mild assumptions on the localized part,
which may contain solitons, breathers, and waves spreading slower than
the free ones.
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