The generation and evolution of lump solitary waves in surface-tension-dominated flows

Kurt M. Berger, Paul A. Milewski

Research output: Contribution to journalArticlepeer-review

51 Citations (SciVal)


Three-dimensional solitary waves or lump solitons are known to be solutions to the Kadomtsev-Petviashvili I equation, which models small-amplitude shallow-water waves when the Bond number is greater than 1/3. Recently, Pego and Quintero presented a proof of the existence of such waves for the Benney-Luke equation with surface tension. Here we establish an explicit connection between the lump solitons of these two equations and numerically compute the Benney-Luke lump solitons and their speed-amplitude relation. Furthermore, we numerically collide two Benney-Luke lump solitons to illustrate their soliton wave character. Finally, we study the flow over an obstacle near the linear shallow-water speed and show that three-dimensional lump solitons are periodically generated.

Original languageEnglish
Pages (from-to)731-750
Number of pages20
JournalSIAM Journal on Applied Mathematics
Issue number3
Publication statusPublished - 1 Jan 2000


  • Capillary-gravity waves
  • Flow over topography
  • Solitary waves

ASJC Scopus subject areas

  • Applied Mathematics


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