Sarbarish Chakravarty, Department of Mathematics, University of Colorado Colorado Springs

Multi-lump solutions of KPI

A class of non-singular rational solutions of the Kadomtsev-Petviashvili (KP) I equation are explicitly constructed. The solutions have multiple peaks which form a two-dimensional wave pattern characterized by the partitions of a positive integer N, which is the number of peaks. The pattern formations are described by the roots of well-known polynomials arising in the study of rational solutions of Painlev II and IV equations.