A simple formula for the conserved charges of soliton theories

Details A simple formula for the conserved charges of soliton theories A simple formula for the conserved charges of soliton theories

2007-07-11

arxiv.org/abs/0707.1603v2

JHEP 0709:015,2007

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, plain latex, 1 eps figure, In this second version the example of the mKdV equation was added in section 4.1, and a p

Scientific paper

10.1088/1126-6708/2007/09/015

We present a simple formula for all the conserved charges of soliton theories, evaluated on the solutions belonging to the orbit of the vacuum under the group of dressing transformations. For pedagogical reasons we perform the explicit calculations for the case of the sine-Gordon model, taken as a prototype of soliton theories. We show that the energy and momentum are boundary terms for all the solutions on the orbit of the vacuum. That orbit includes practically all the solutions of physical interest, namely solitons, multi-solitons, breathers, and combinations of solitons and breathers. The example of the mKdV equation is also given explicitly.

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