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

Dmitry Strunin

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 a point. The soliton was suggested as a model of 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 process of soliton formation and analysed its structure.

Full Text:

PDF BibTeX


DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1454



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.