Lump chains in the KP-I equation

Charles Lester, Dmitry Zakharov

Research output: Contribution to journalArticlepeer-review


We construct a broad class of solutions of the Kadomtsev–Petviashvili (KP)-I equation by using a reduced version of the Grammian form of the (Formula presented.) -function. The basic solution is a linear periodic chain of lumps propagating with distinct group and wave velocities. More generally, our solutions are evolving linear arrangements of lump chains, and can be viewed as the KP-I analogues of the family of line-soliton solutions of KP-II. However, the linear arrangements that we construct for KP-I are more general, and allow degenerate configurations such as parallel or superimposed lump chains. We also construct solutions describing interactions between lump chains and individual lumps, and discuss the relationship between the solutions obtained using the reduced and regular Grammian forms.

Original languageEnglish
Pages (from-to)1425-1442
JournalStudies in Applied Mathematics
Issue number4
StatePublished - 2021


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