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Article: Logarithmic nonlinear Schro••dinger equation and irrotational, compressible flows: An exact solution

TitleLogarithmic nonlinear Schro••dinger equation and irrotational, compressible flows: An exact solution
Authors
KeywordsDinger equation
Exact solution
Explicit expressions
Fluid property
Function of time
Issue Date2011
PublisherAmerican Physical Society. The Journal's web site is located at http://pre.aps.org
Citation
Physical Review E - Statistical, Nonlinear, And Soft Matter Physics, 2011, v. 84 n. 1 How to Cite?
AbstractA class of irrotational, isentropic, and compressible flows is studied theoretically by formulating the density and the velocity potential in a Madelung transformation. The resulting nonlinear Schrödinger equation is solved in terms of similarity variables. One particular family of exact solutions, valid for any ratio of the specific heat capacities of the gas, permits explicit expressions of the fluid properties and velocities in terms of time and spatial coordinates. Analytically, the density is a Gaussian function of the similarity variable, while the temperature is a function of time only. This method is applicable in one (1D), two, and three dimensional geometries. As a simple example, a 1D gas column, with mass injection on one side and a steadily translating wall on the other, can be formulated exactly. The connection with the evolution of an unsteady velocity potential will also be examined. © 2011 American Physical Society.
Persistent Identifierhttp://hdl.handle.net/10722/137330
ISSN
2014 Impact Factor: 2.288
2015 SCImago Journal Rankings: 0.999
ISI Accession Number ID
Funding AgencyGrant Number
Research Grants CouncilHKU 7120/08E
Funding Information:

The author would like to thank Professor Colin Rogers for introducing this subject to his research group. Partial financial support is provided by the Research Grants Council Contract No. HKU 7120/08E.

References

 

DC FieldValueLanguage
dc.contributor.authorChow, KWen_HK
dc.date.accessioned2011-08-26T14:23:26Z-
dc.date.available2011-08-26T14:23:26Z-
dc.date.issued2011en_HK
dc.identifier.citationPhysical Review E - Statistical, Nonlinear, And Soft Matter Physics, 2011, v. 84 n. 1en_HK
dc.identifier.issn1539-3755en_HK
dc.identifier.urihttp://hdl.handle.net/10722/137330-
dc.description.abstractA class of irrotational, isentropic, and compressible flows is studied theoretically by formulating the density and the velocity potential in a Madelung transformation. The resulting nonlinear Schrödinger equation is solved in terms of similarity variables. One particular family of exact solutions, valid for any ratio of the specific heat capacities of the gas, permits explicit expressions of the fluid properties and velocities in terms of time and spatial coordinates. Analytically, the density is a Gaussian function of the similarity variable, while the temperature is a function of time only. This method is applicable in one (1D), two, and three dimensional geometries. As a simple example, a 1D gas column, with mass injection on one side and a steadily translating wall on the other, can be formulated exactly. The connection with the evolution of an unsteady velocity potential will also be examined. © 2011 American Physical Society.en_HK
dc.languageengen_US
dc.publisherAmerican Physical Society. The Journal's web site is located at http://pre.aps.orgen_HK
dc.relation.ispartofPhysical Review E - Statistical, Nonlinear, and Soft Matter Physicsen_HK
dc.rightsPhysical Review E (Statistical, Nonlinear, and Soft Matter Physics). Copyright © American Physical Society.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectDinger equation-
dc.subjectExact solution-
dc.subjectExplicit expressions-
dc.subjectFluid property-
dc.subjectFunction of time-
dc.titleLogarithmic nonlinear Schro••dinger equation and irrotational, compressible flows: An exact solutionen_HK
dc.typeArticleen_HK
dc.identifier.emailChow, KW:kwchow@hku.hken_HK
dc.identifier.authorityChow, KW=rp00112en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1103/PhysRevE.84.016308en_HK
dc.identifier.pmid21867305-
dc.identifier.scopuseid_2-s2.0-79961148620en_HK
dc.identifier.hkuros189596en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79961148620&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume84en_HK
dc.identifier.issue1en_HK
dc.identifier.eissn1550-2376-
dc.identifier.isiWOS:000293414300006-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChow, KW=13605209900en_HK

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