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Article: New integrability case for the Riccati equation

TitleNew integrability case for the Riccati equation
Authors
Mak, MKHarko, T
KeywordsAuxiliary equations
Damped harmonic oscillator
General solutions
Generating functions
Integrability
Issue Date2012
PublisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/amc
Citation
Applied Mathematics and Computation, 2012, v. 218 n. 22, p. 10974-10981 How to Cite?
DOI: http://dx.doi.org/10.1016/j.amc.2012.04.058
AbstractA new integrability condition of the Riccati equation dy/dx=a(x)+b(x)y+c(x) y2 is presented. By introducing an auxiliary equation depending on a generating function f(x), the general solution of the Riccati equation can be obtained if the coefficients a(x), b(x), c(x), and the function f(x) satisfy a particular constraint. The validity and reliability of the method are tested by obtaining the general solutions of some Riccati type differential equations. Some applications of the integrability conditions for the case of the damped harmonic oscillator with time dependent frequency, and for solitonic wave, are briefly discussed. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/159791
ISSN
0096-3003
2021 Impact Factor: 4.397
2020 SCImago Journal Rankings: 0.972
ISI Accession Number ID
WOS:000305800700017

 

DC FieldValueLanguage
dc.contributor.authorMak, MKen_US
dc.contributor.authorHarko, Ten_US
dc.date.accessioned2012-08-16T05:56:39Z-
dc.date.available2012-08-16T05:56:39Z-
dc.date.issued2012en_US
dc.identifier.citationApplied Mathematics and Computation, 2012, v. 218 n. 22, p. 10974-10981en_US
dc.identifier.issn0096-3003-
dc.identifier.urihttp://hdl.handle.net/10722/159791-
dc.description.abstractA new integrability condition of the Riccati equation dy/dx=a(x)+b(x)y+c(x) y2 is presented. By introducing an auxiliary equation depending on a generating function f(x), the general solution of the Riccati equation can be obtained if the coefficients a(x), b(x), c(x), and the function f(x) satisfy a particular constraint. The validity and reliability of the method are tested by obtaining the general solutions of some Riccati type differential equations. Some applications of the integrability conditions for the case of the damped harmonic oscillator with time dependent frequency, and for solitonic wave, are briefly discussed. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.-
dc.languageengen_US
dc.publisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/amcen_US
dc.relation.ispartofApplied Mathematics and Computationen_US
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, 2012, v. 218 n. 22, p. 10974-10981. DOI: 10.1016/j.amc.2012.04.058-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectAuxiliary equations-
dc.subjectDamped harmonic oscillator-
dc.subjectGeneral solutions-
dc.subjectGenerating functions-
dc.subjectIntegrability-
dc.titleNew integrability case for the Riccati equationen_US
dc.typeArticleen_US
dc.identifier.emailMak, MK: mkmak@vtc.edu.hken_US
dc.identifier.emailHarko, T: harko@hkucc.hku.hk-
dc.identifier.authorityHarko, TC=rp01333en_US
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.amc.2012.04.058-
dc.identifier.scopuseid_2-s2.0-84862836275-
dc.identifier.hkuros203995en_US
dc.identifier.volume218en_US
dc.identifier.issue22-
dc.identifier.spage10974en_US
dc.identifier.epage10981en_US
dc.identifier.isiWOS:000305800700017-
dc.publisher.placeUnited States-
dc.identifier.citeulike10836677-
dc.identifier.issnl0096-3003-

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