Non-crossing permutations for the KP solitons under the Gel'fand-Dickey reductions and the vertex operators

Shilong Huang, Yuji Kodama, Chuanzhong Li

We give a classification of the $regular$ soliton solutions of the KP hierarchy, referred to as the $KPsolitons$, under the Gel'fand-Dickey $\ell$-reductions in terms of the permu…