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# Interaction of two lump solitons described by the Kadomtsev-Petviashvili I equation

preprint

posted on 2005-08-01, 12:45 authored by Zhiming Lu, Emily M. Tian, Roger GrimshawThe interaction of two lump solitons described by the Kadomtsev-Petviashvili I(KPI)
equation is analyzed using both exact and numerical methods. The numerical method
is based on a third order Runge-Kutta method, and a Crank- Nicholson scheme. The
main characteristic of a direct interaction when the two lumps are initially aligned along
the x-axis, is that they may separate in the y-direction, but then come back to the xaxis
after collision; the dependence of the maximum separation in the y-direction on
the relative velocity difference is described. Two lumps may also experience an abrupt
phase change in the case of an oblique interaction.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

1732902 bytes## Publication date

2003## Notes

This pre-print has been submitted, and accepted to the journal, Wave Motion [© Elsevier]. The definitive version: LU, Z., TIAN, E.M. and GRIMSHAW, R., 2004. Interaction of two lump solitons described by the Kadomtsev-Petviashvili I equation. Wave Motion,40(2), pp. 123-135, is available at: http://www.sciencedirect.com/science/journal/01652125.## Language

- en