Exact Noncommutative KP and KdV Multi-solitons

Details Exact Noncommutative KP and KdV Multi-solitons Exact Noncommutative KP and KdV Multi-solitons

2001-05-18

arxiv.org/abs/hep-th/0105185v2

Physics

High Energy Physics

High Energy Physics - Theory

18 pages LaTeX. Reference added

Scientific paper

We derive the Kadomtsev-Petviashvili (KP) equation defined over a general associative algebra and construct its N-soliton solution. For the example of the Moyal algebra, we find multi-soliton solutions for arbitrary space-space noncommutativity. The noncommutativity of coordinates is shown to obstruct the general construction of a tau function for these solitons. We investigate the two-soliton solution in detail and show that asymptotic observers of soliton scattering are unable to detect a finite spatial noncommutativity. An explicit example shows that a pair of solitons in a noncommutative background can be interpreted as several pairs of image solitons. Finally, a dimensional reduction gives the general N-soliton solution for the previously discussed noncommutative KdV equation.

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