Seminar 27.05.2026: Chuanzhong Li (Shandong University of Science and Technology, China)

Title: Classifications on soliton solutions of KP type systems Abstract: In this talk, we will give a classification of the regular soliton solutions of the KP hierarchy, referred to as the KP solitons, under the Gel'fand-Dickey reductions in terms of the permutation of the symmetric group. As an example, we show that the regular soliton solutions of the (good) Boussinesq equation as the 3-reduction can have at most one resonant soliton. In particular, we show that the non-crossing permutation gives the regularity condition for the soliton solutions. Meanwhile the classification on singular soliton solutions of the Boussinesq equation is also interesting.