Abstract
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.
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