q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics
type: Item
instance of: scholarly article
title: q-Gaussian integrable Hamiltonian reductions in anisentropic gasdynamics
zbMATH Open document ID: 1303.37026
author: Colin Rogers
author: Tomasso Ruggeri
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2014-12-04T00:00:00Z
review text: The present paper is devoted to a special kind of \(q\)-logarithmic nonlinear Schrödinger (NLS) type equation which incorporates a de Broglie-Bohm quantum potential term, derived in the framework of spatial anisentropic gasdynamics. In the limit \(q\rightarrow 1\) and in the absence of the de Broglie-Bohm term the well-known logarithmic NLS equation is retrieved. The physical motivation for the present study stems from an investigation into spinning gas cloud evolution.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 76B47
zbMATH DE Number: 6376806
zbMATH Keywords: \(q\)-Gaussian integrability
zbMATH Keywords: Tsallis statistical mechanics
zbMATH Keywords: gasdynamics
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: dcdsb.2014.19.2297
OpenAlex ID: W2321878490
cites work: Gaussons: Solitons of the Logarithmic Schrödinger Equation
cites work: A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
cites work: Tsallis' maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
cites work: Q5594493
cites work: Expanding gas clouds of ellipsoidal shape: new exact solutions
cites work: Spinning gas clouds with precession: a new formulation
cites work: Q4827369
cites work: Soliton Management in Periodic Systems
cites work: Generalised Thermostatistics
cites work: Soliton resonances in a generalized nonlinear Schrödinger equation
cites work: Q5811877
cites work: Ermakov systems, nonlinear superposition, and solutions of nonlinear equations of motion
cites work: On (2+1)-dimensional Ermakov systems
cites work: Multi-component Ermakov systems: Structure and linearization
cites work: Ermakov-Ray-Reid Systems in (2+1)-Dimensional Rotating Shallow Water Theory
cites work: Ermakov–Ray–Reid systems in nonlinear optics
cites work: The pulsrodon in 2+1-dimensional magneto-gasdynamics: Hamiltonian structure and integrability
cites work: On the integrability of a Hamiltonian reduction of a 2+1-dimensional non-isothermal rotating gas cloud system
cites work: Ermakov–Ray–Reid Reductions of Variational Approximations in Nonlinear Optics
cites work: On a (2+1)-dimensional Madelung system with logarithmic and with Bohm quantum potentials: Ermakov reduction
cites work: On complex-lamellar motion of a Prim gas
cites work: Ermakov systems of arbitrary order and dimension: structure and linearization
cites work: Universal and Integrable Aspects of an Elliptic Vortex Representation in 2+1‐Dimensional Magneto‐Gasdynamics
cites work: Introduction to Nonextensive Statistical Mechanics
DOI: 10.3934/DCDSB.2014.19.2297
Recommended article: On \(q\)-Gaussian integrable Hamiltonian reductions in anisentropic magneto-gasdynamics
Recommended article: A q-deformed completely integrable Bose gas model
Recommended article: Gaussian ensemble for quantum integrable dynamics
Recommended article: Integrable quantum hydrodynamics in two-dimensional phase space
Recommended article: Singularly perturbed Hamiltonians of a quantum Rayleigh gas defined as quadratic forms
Recommended article: On the Gupta-Bleuler quantization of the Hamiltonian systems with anomalies
Recommended article: Asymptotic behaviors of the full quantum hydrodynamic equations
Recommended article: Renormalization group reduction of non-integrable Hamiltonian systems
Recommended article: Quantum quenches in integrable systems: constraints from factorisation
Recommended article: Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas
description: scientific article; zbMATH DE number 6376806