Lump chains in the KP-I equation

Charles Lester, Andrey Gelash, Dmitry Zakharov, Vladimir Zakharov

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


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 (US)
Pages (from-to)1425-1442
Number of pages18
JournalStudies in Applied Mathematics
Issue number4
StatePublished - Nov 2021


  • Grammian form
  • line-solitons
  • lump solutions
  • tau-function

ASJC Scopus subject areas

  • Applied Mathematics


Dive into the research topics of 'Lump chains in the KP-I equation'. Together they form a unique fingerprint.

Cite this