In this talk, we study the scattering problem for the initial value problem
of the generalized Korteweg-de Vries (gKdV) equation. The purpose of
this talk is to achieve two primary goals. Firstly, we show small data scattering
for (gKdV) in the weighted Sobolev space, ensuring the initial and
the asymptotic states belong to the same class. Secondly, we introduce
two equivalent characterizations of scattering in the weighted Sobolev space.
In particular, this involves the so-called conditional scattering in the weighted
Sobolev space. This talk is based on a joint work with Satoshi Masaki (Hokkaido University)
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