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Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions

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  • Yair Zarmi

Abstract

Slower-than-light multi-front solutions of the Sine-Gordon in (1+2) dimensions, constructed through the Hirota algorithm, are mapped onto spatially localized structures, which emulate free, spatially extended, massive relativistic particles. A localized structure is an image of the junctions at which the fronts intersect. It propagates together with the multi-front solution at the velocity of the latter. The profile of the localized structure obeys the linear wave equation in (1+2) dimensions, to which a term that represents interaction with a slower-than-light, Sine-Gordon-multi-front solution has been added. This result can be also formulated in terms of a (1+2)-dimensional Lagrangian system, in which the Sine-Gordon and wave equations are coupled. Expanding the Euler-Lagrange equations in powers of the coupling constant, the zero-order part of the solution reproduces the (1+2)-dimensional Sine-Gordon fronts. The first-order part is the spatially localized structure. PACS: 02.30.Ik, 03.65.Pm, 05.45.Yv, 02.30.Ik.

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  • Yair Zarmi, 2016. "Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-17, March.
    • Handle: RePEc:plo:pone00:0148993
    DOI: 10.1371/journal.pone.0148993
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    References listed on IDEAS

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    1. Yun-Mei Zhao, 2014. "Exact Solutions of Coupled Sine-Gordon Equations Using the Simplest Equation Method," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-5, February.
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