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

Strunin, D. V. (2008) Two-dimensional particle solution of the extended Hamilton-Jacobi equation. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 50. C282-C291. ISSN 1446-8735

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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.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author's version deposited in accordance with the copyright polciy of the publisher.
Depositing User: Dr Dmitry Strunin
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 12 Nov 2009 06:52
Last Modified: 02 Jul 2013 23:15
Uncontrolled Keywords: extended Hamilton-Jacobi equation, soliton solution
Fields of Research (FOR2008): 01 Mathematical Sciences > 0105 Mathematical Physics > 010503 Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory
01 Mathematical Sciences > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified

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