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

Dmitry Strunin


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.

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.