A simple formula for the conserved charges of soliton theories

Ferreira, Luiz Agostinho; Zakrzewski, W.J.

Abstract

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.

Citation

Ferreira, L. A., & Zakrzewski, W. (2007). A simple formula for the conserved charges of soliton theories. Journal of High Energy Physics, 2007(09), https://doi.org/10.1088/1126-6708/2007/09/015

• Journal Article Type: Article
• Acceptance Date: Aug 25, 2007
• Publication Date: Sep 3, 2007
• Deposit Date: Sep 21, 2007
• Publicly Available Date: Jun 17, 2015
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2007
• Issue: 09
• DOI: https://doi.org/10.1088/1126-6708/2007/09/015
• Keywords: Integrable hierarchies, Integrable equations in physics, Integrable field theories.
• Public URL: https://durham-repository.worktribe.com/output/1567824
• Related Public URLs: http://arxiv.org/abs/0707.1603