Abstract
The connection between the theory of integer partitions and a class of nonsingular rational solutions of the Kadomtsev–Petviashvili (KP) I equation referred to as multi-lumps is investigated. It is shown that specific partitions of a given positive integer N lead to multi-lump solutions that exhibit distinctive surface wave patterns. The pattern formations are described by the complex roots of special polynomials such as the Yablonskii–Vorob’ev, Okamoto and generalized Okamoto polynomials arising in the study of rational solutions of Painlevé II and IV equations. Stationary KPI multi-lumps which correspond to rational solutions of the Boussinesq equation are also discussed.
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