Two-dimensional particle solution of the extended Hamilton-Jacobi equation

Article

Strunin, D. V.. 2008. "Two-dimensional particle solution of the extended Hamilton-Jacobi equation." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 50 (August), pp. C282-C291.
Article Title

Two-dimensional particle solution of the extended Hamilton-Jacobi equation

ERA Journal ID43
Article CategoryArticle
Authors
AuthorStrunin, D. V.
Journal TitleAustralian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Journal Citation50 (August), pp. C282-C291
Number of Pages10
Year2008
Place of PublicationCambridge, United Kingdom
ISSN1446-1811
1446-8735
Web Address (URL)http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1454
Abstract

In classical mechanics the Hamilton-Jacobi equation for a free particle has the property of reducing a perturbation of spatially uniform solution into a point. In the late 1970s Sivashinsky proposed an extension of the equation so that it takes the form of the Kuramoto-Sivashinsky equation under which a smooth soliton is formed instead of the point. The soliton was proposed as a model for spatially extended elementary particle. However, this solution is unstable. Developing the Sivashinsky's idea further, we propose a different extension which ensures stability. We performed two-dimensional computational
experiments demonstrating the soliton formation and stability.

Keywordsextended Hamilton-Jacobi equation; soliton solution; particle physics
ANZSRC Field of Research 2020490203. Mathematical aspects of classical mechanics, quantum mechanics and quantum information theory
510703. Particle physics
490109. Theoretical and applied mechanics
Public Notes

© Australian Mathematical Society 2008. This publication is copyright. It may be reproduced in whole or in part for the purposes of study, research, or review, but is subject to the inclusion of an acknowledgment of the source. Author's version deposited in accordance with the copyright polciy of the publisher.

Byline AffiliationsDepartment of Mathematics and Computing
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