Volume 113, Number 5, March 2016
|Number of page(s)||5|
|Published online||01 April 2016|
Dissipative effects in nonlinear Klein-Gordon dynamics
1 CeBio y Secretaría de Investigación, Universidad Nacional Buenos Aires- Noreoeste (UNNOBA) and Conicet Roque Saenz Peña 456, Junin, Argentina
2 Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro - RJ, Brazil
3 Santa Fe Institute - 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Received: 10 January 2016
Accepted: 22 March 2016
We consider dissipation in a recently proposed nonlinear Klein-Gordon dynamics that admits exact time-dependent solutions of the power-law form , involving the q-exponential function naturally arising within the nonextensive thermostatistics (, with ). These basic solutions behave like free particles, complying, for all values of q, with the de Broglie-Einstein relations , and satisfying a dispersion law corresponding to the relativistic energy-momentum relation . The dissipative effects explored here are described by an evolution equation that can be regarded as a nonlinear generalization of the celebrated telegraph equation, unifying within one single theoretical framework the nonlinear Klein-Gordon equation, a nonlinear Schrödinger equation, and the power-law diffusion (porous-media) equation. The associated dynamics exhibits physically appealing traveling solutions of the q-plane wave form with a complex frequency ω and a q-Gaussian square modulus profile.
PACS: 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05) / 02.30.Jr – Partial differential equations / 03.50.-z – Classical field theories
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