Decay of Kadomtsev - Petviashvili lumps in dissipative media

TL;DR

This paper investigates how various dissipative effects cause the decay and instability of Kadomtsev-Petviashvili lumps, combining analytical asymptotic theory with numerical simulations for validation.

Contribution

It provides the first detailed analysis of lump decay under multiple dissipative mechanisms and compares analytical predictions with numerical results for two key dissipation models.

Findings

Lumps are unstable under dissipation.

Analytical and numerical results agree well.

Trajectories are calculated for Rayleigh and Reynolds dissipation.

Abstract

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.