q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics

Colin Rogers; Tommaso Ruggeri

doi:10.3934/dcdsb.2014.19.2297

Article Contents

2014, Volume 19, Issue 7: 2297-2312. Doi: 10.3934/dcdsb.2014.19.2297

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q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics

Colin Rogers^1, and
Tommaso Ruggeri^2,

1.
Australian Research Council Centre of Excellence for Mathematics & Statistics of Complex Systems, School of Mathematics, The University of New South Wales, Sydney, NSW2052
2.
Department of Mathematics & Research Centre of Applied Mathematics (CIRAM), University of Bologna

Received: February 28, 2013

Revised: February 28, 2014

Published: August 2014

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Abstract

Integrable reductions in non-isothermal spatial gasdynamics are isolated corresponding to q-Gaussian density distributions. The availability of a Tsallis parameter q in the reductions permits the construction via a Madelung transformation of wave packet solutions of a class of associated q-logarithmic nonlinear Schrödinger equations involving a de Broglie-Bohm quantum potential term.

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Mathematics Subject Classification: 37K10, 76B47.

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