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

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.