Decay of Kadomtsev–Petviashvili lumps in dissipative media

S. Clarke, K. Gorshkov, R. Grimshaw, Y. Stepanyants

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13 Citations (Scopus)


The decay of Kadomtsev–Petviashvili lumps is considered for a few typical dissipations—Rayleigh dissipation, Reynolds dissipation, Landau damping, Chezy bottom friction, viscous dissipation in the laminar boundary layer, and radiative losses caused by large-scale dispersion. It is shown that the straight-line motion of lumps is unstable under the influence of dissipation. The lump trajectories are calculated for two most typical models of dissipation—the Rayleigh and Reynolds dissipations. A comparison of analytical results obtained within the framework of asymptotic theory with the direct numerical calculations of the Kadomtsev–Petviashvili equation is presented. Good agreement between the theoretical and numerical results is obtained.

Original languageEnglish
Pages (from-to)43-50
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Publication statusPublished - 1 Mar 2018


  • Adiabatic theory
  • Dissipation
  • Kadomtsev–Petviashvili equation
  • Lump
  • Numerical calculations
  • Soliton

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