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arXiv · 1510.00415

Dissipative Effects in Nonlinear Klein-Gordon Dynamics

A. R. Plastino·C. Tsallis
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Abstract

We consider dissipation in a recently proposed nonlinear Klein-Gordon dynamics that admits soliton-like solutions of the power-law form $e_q^{i(kx-wt)}$, involving the $q$-exponential function naturally arising within the nonextensive thermostatistics [$e_q^z \equiv [1+(1-q)z]^{1/(1-q)}$, with $e_1^z=e^z$]. These basic solutions behave like free particles, complying, for all values of $q$, with the de Broglie-Einstein relations $p=\hbar k$, $E=\hbar ω$ and satisfying a dispersion law corresponding to the relativistic energy-momentum relation $E^2 = c^2p^2 + m^2c^4 $. The dissipative effects explored here are described by an evolution equation that can be regarded as a nonlinear version of the celebrated telegraphists equation, unifying within one single theoretical framework the nonlinear Klein-Gordon equation, a nonlinear Schroedinger equation, and the power-law diffusion (porous media) equation. The associated dynamics exhibits physically appealing soliton-like traveling solutions of the $q$-plane wave form with a complex frequency $ω$ and a $q$-Gaussian square modulus profile.

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A. R. Plastino, C. Tsallis. 2015-10-01. Dissipative Effects in Nonlinear Klein-Gordon Dynamics. https://doi.org/10.1209/0295-5075%2F113%2F50005

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