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Article: New further integrability cases for the Riccati equation
Title | New further integrability cases for the Riccati equation |
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Authors | |
Keywords | Riccati equation Integrability condition Applications in physics |
Issue Date | 2013 |
Publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/amc |
Citation | Applied Mathematics and Computation, 2013, v. 219 n. 14, p. 7465-7471 How to Cite? |
Abstract | New further integrability conditions of the Riccati equation dy/dx=a(x)+b(x)y+c(x)y2 are presented. The first case corresponds to fixed functional forms of the coefficients a(x) and c(x) of the Riccati equation, and of the function F(x)=a(x)+f(x)-b2(x)/4c(x), where f(x) is an arbitrary function. The second integrability case is obtained for the 'reduced' Riccati equation with b(x)≡0. If the coefficients a(x) and c(x) satisfy the condition ±d√f(x)/c(x)/dx=a(x)+f(x), where f(x) is an arbitrary function, then the general solution of the 'reduced' Riccati equation can be obtained by quadratures. The applications of the integrability condition of the 'reduced' Riccati equation for the integration of the Schrödinger and Navier-Stokes equations are briefly discussed. |
Persistent Identifier | http://hdl.handle.net/10722/183148 |
ISSN | 2023 Impact Factor: 3.5 2023 SCImago Journal Rankings: 1.026 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Mak, MK | - |
dc.contributor.author | Harko, TC | - |
dc.date.accessioned | 2013-05-15T01:45:23Z | - |
dc.date.available | 2013-05-15T01:45:23Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | Applied Mathematics and Computation, 2013, v. 219 n. 14, p. 7465-7471 | - |
dc.identifier.issn | 0096-3003 | - |
dc.identifier.uri | http://hdl.handle.net/10722/183148 | - |
dc.description.abstract | New further integrability conditions of the Riccati equation dy/dx=a(x)+b(x)y+c(x)y2 are presented. The first case corresponds to fixed functional forms of the coefficients a(x) and c(x) of the Riccati equation, and of the function F(x)=a(x)+f(x)-b2(x)/4c(x), where f(x) is an arbitrary function. The second integrability case is obtained for the 'reduced' Riccati equation with b(x)≡0. If the coefficients a(x) and c(x) satisfy the condition ±d√f(x)/c(x)/dx=a(x)+f(x), where f(x) is an arbitrary function, then the general solution of the 'reduced' Riccati equation can be obtained by quadratures. The applications of the integrability condition of the 'reduced' Riccati equation for the integration of the Schrödinger and Navier-Stokes equations are briefly discussed. | - |
dc.language | eng | - |
dc.publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/amc | - |
dc.relation.ispartof | Applied Mathematics and Computation | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Riccati equation | - |
dc.subject | Integrability condition | - |
dc.subject | Applications in physics | - |
dc.title | New further integrability cases for the Riccati equation | - |
dc.type | Article | - |
dc.identifier.email | Mak, MK: mkmak@vtc.edu.hk | - |
dc.identifier.email | Harko, TC: t.harko@ucl.ac.uk | - |
dc.identifier.authority | Harko, TC=rp01333 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1016/j.amc.2013.01.033 | - |
dc.identifier.scopus | eid_2-s2.0-84875937744 | - |
dc.identifier.hkuros | 214362 | - |
dc.identifier.volume | 219 | - |
dc.identifier.issue | 14 | - |
dc.identifier.spage | 7465 | - |
dc.identifier.epage | 7471 | - |
dc.identifier.isi | WOS:000316668800019 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0096-3003 | - |