コロキウム

Solitary wave solutions called solitons in integrable PDEs have attracted much attention since their discovery in the 60s. Such PDEs can be written in Lax pairs and solved by the inverse scattering transform (IST). In this talk, we consider the KdV equation, which is one of the most famous integrable PDEs, and study singular solitary waves, among which rational solitons, positons, negatons, and complexitons are known as typical ones. We show that for negatons the reflection coefficients are zero and the transmission coefficients have multiple zeros in general, and that the IST can be carried out rigorously when the reflection coefficients are zero even if the transmission coefficients have multiple zeros. This is joint work with Katsuki Kobayashi.