Construction and analysis of multi-lump solutions of dispersive long wave equations via integer partitions

In this paper, the relation between the integer partition theory and a kind of rational solution of the dispersion long wave equations is studied. For the integer partition {\lambda}= ({\lambda}1,{\lambda}2,... ,{\lambda}n) of positive integer N, with the degree vector m = (m1,m2,... ,mn), the corresponding M lump solution can be obtained where M = N + n mn. Combined with the generalized Schur polynomial and heat polynomial, the asymptotic positions of peaks are studied, and the arrangement of multi-peak groups in multi-lump solutions are obtained, as well as the relationship between the patterns formed by single-peak groups and the corresponding integer partition.