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

TL;DR

This paper explores the connection between integer partition theory and rational multi-lump solutions of dispersive long wave equations, revealing how integer partitions influence solution patterns and peak arrangements.

Contribution

It introduces a novel method linking integer partitions to multi-lump solutions, analyzing their asymptotic peak positions and pattern formations.

Findings

Multi-lump solutions are characterized by integer partitions.

Asymptotic peak positions depend on partition structure.

Patterns of peaks relate to specific integer partitions.

Abstract

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.