Painlevé Test, Generalized Symmetries, Bäcklund Transformations and Exact Solutions to the Third-Order Burgers’ Equations
In this paper, the Painlevé analysis is performed on the physical form of the third-order Burgers’ equation, the Painlevé property and integrability (C-integrable) of the equation is verified. Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other...
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| Published in | Journal of statistical physics Vol. 158; no. 2; pp. 433 - 446 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.01.2015
Springer |
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| Online Access | Get full text |
| ISSN | 0022-4715 1572-9613 |
| DOI | 10.1007/s10955-014-1130-8 |
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| Abstract | In this paper, the Painlevé analysis is performed on the physical form of the third-order Burgers’ equation, the Painlevé property and integrability (C-integrable) of the equation is verified. Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other equation are given by the symmetry transformation method. The Bäcklund Transformations of the equations are constructed based on the symmetries, respectively. Furthermore, the exact explicit solutions to the equations are investigated in terms of the symmetries, Bäcklund transformations and transformations of the equations. |
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| AbstractList | In this paper, the Painleve analysis is performed on the physical form of the third-order Burgers' equation, the Painleve property and integrability (C-integrable) of the equation is verified. Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other equation are given by the symmetry transformation method. The Backlund Transformations of the equations are constructed based on the symmetries, respectively. Furthermore, the exact explicit solutions to the equations are investigated in terms of the symmetries, Backlund transformations and transformations of the equations. Keywords Third-order Burger's equation * Integrability * Generalized symmetry * Backlund transformation * Exact solution Mathematics Subject Classification 17B80 * 22E70 * 35C05 In this paper, the Painlevé analysis is performed on the physical form of the third-order Burgers’ equation, the Painlevé property and integrability (C-integrable) of the equation is verified. Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other equation are given by the symmetry transformation method. The Bäcklund Transformations of the equations are constructed based on the symmetries, respectively. Furthermore, the exact explicit solutions to the equations are investigated in terms of the symmetries, Bäcklund transformations and transformations of the equations. |
| Audience | Academic |
| Author | Liu, Hanze |
| Author_xml | – sequence: 1 givenname: Hanze surname: Liu fullname: Liu, Hanze email: hzliumath@hotmail.com organization: School of Mathematical Sciences, Liaocheng University, Department of Mathematics, Binzhou University |
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| Cites_doi | 10.1088/0266-5611/3/2/008 10.1016/0167-2789(87)90046-7 10.1007/s12190-012-0633-1 10.1063/1.525721 10.1088/0253-6102/57/5/02 10.1016/j.cam.2008.06.009 10.1016/0167-2789(89)90040-7 10.1016/j.na.2009.01.075 10.1007/s11071-009-9556-2 10.1016/j.jde.2012.12.004 10.1093/imamat/44.1.27 10.1007/BF02798794 |
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| References | Clarkson (CR7) 1990; 44 Liu, Li, Liu (CR13) 2010; 59 Liu, Li, Liu (CR14) 2012; 22 Wang, Guo (CR20) 2000 Liu, Li, Zhang (CR1) 2009; 228 Chou (CR10) 1987; 10 Liu, Li, Liu (CR15) 2012; 57 Polyanin, Zaitsev (CR21) 2003 Calogero, Eckhaus (CR19) 1987; 3 Cariello, Tabor (CR6) 1989; 39 Fokas, Fuchssteiner (CR17) 1980; 28 Tian (CR18) 1989; 12 Newell (CR5) 1987; 29 Bluman, Anco (CR9) 2002 Conte, Musette (CR3) 2008 Olver (CR8) 1993 Cheng (CR11) 1991; 14 Weiss, Tabor, Carnevale (CR4) 1983; 24 Liu, Geng (CR16) 2013; 254 Liu, Li, Liu (CR2) 2013; 42 Liu, Li (CR12) 2009; 71 R Conte (1130_CR3) 2008 F Cariello (1130_CR6) 1989; 39 C Tian (1130_CR18) 1989; 12 H Liu (1130_CR13) 2010; 59 H Liu (1130_CR1) 2009; 228 J Weiss (1130_CR4) 1983; 24 P Olver (1130_CR8) 1993 H Liu (1130_CR14) 2012; 22 H Liu (1130_CR2) 2013; 42 H Liu (1130_CR16) 2013; 254 Z Wang (1130_CR20) 2000 T Chou (1130_CR10) 1987; 10 P Clarkson (1130_CR7) 1990; 44 G Bluman (1130_CR9) 2002 A Fokas (1130_CR17) 1980; 28 A Newell (1130_CR5) 1987; 29 H Liu (1130_CR12) 2009; 71 Y Cheng (1130_CR11) 1991; 14 A Polyanin (1130_CR21) 2003 H Liu (1130_CR15) 2012; 57 F Calogero (1130_CR19) 1987; 3 |
| References_xml | – year: 2008 ident: CR3 publication-title: The Painlevé Handbook – year: 2003 ident: CR21 publication-title: Handbook of Exact Solutions for Ordinary Differential Equations – volume: 3 start-page: 229 year: 1987 end-page: 262 ident: CR19 article-title: Nonlinear evolution equations, rescalings, model PDEs and their integrability: I publication-title: Inverse Probl. doi: 10.1088/0266-5611/3/2/008 – volume: 29 start-page: 1 year: 1987 end-page: 68 ident: CR5 article-title: A unified approach to Painlevé expansions publication-title: Physics D doi: 10.1016/0167-2789(87)90046-7 – volume: 12 start-page: 238 year: 1989 end-page: 249 ident: CR18 article-title: Transformation of equations and transformation of symmetries publication-title: Acta Math. Appl. Sin. – volume: 14 start-page: 180 year: 1991 end-page: 184 ident: CR11 article-title: Connections among symmetries, Bäcklund transformation and the Painlevé property for Burgers’ hierarchies publication-title: Acta Math. Appl. Sin. – volume: 42 start-page: 159 year: 2013 end-page: 170 ident: CR2 article-title: The recursion operator method for generalized symmetries and Bäcklund transformations of the Burgers’ equations publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-012-0633-1 – volume: 24 start-page: 522 year: 1983 end-page: 526 ident: CR4 article-title: The Painlevé property for partial differential equations publication-title: J. Math. Phys. doi: 10.1063/1.525721 – volume: 57 start-page: 737 year: 2012 end-page: 742 ident: CR15 article-title: Lie symmetry analysis, Bäcklund transformations and exact solutions to (2 + 1)-dimensional Burgers’ types of equations publication-title: Commun. Theor. Phys. doi: 10.1088/0253-6102/57/5/02 – volume: 228 start-page: 1 year: 2009 end-page: 9 ident: CR1 article-title: Lie symmetry analysis and exact explicit solutions for general Burgers’ equation publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2008.06.009 – volume: 39 start-page: 77 year: 1989 end-page: 94 ident: CR6 article-title: The Painlevé expansions for nonintegrable evolution equations publication-title: Physics D doi: 10.1016/0167-2789(89)90040-7 – volume: 10 start-page: 1009 year: 1987 end-page: 1018 ident: CR10 article-title: New strong symmetries, symmetries and Lie algebra for Burgers’ equation publication-title: Sci. China Ser. A – year: 2000 ident: CR20 article-title: Introduction to special functions publication-title: The Series of Advanced Physics of Peking University – volume: 71 start-page: 2126 year: 2009 end-page: 2133 ident: CR12 article-title: Lie symmetry analysis and exact solutions for the short pulse equation publication-title: Nonlinear Anal. TMA doi: 10.1016/j.na.2009.01.075 – volume: 22 start-page: 1 issue: 1250188 year: 2012 end-page: 11 ident: CR14 article-title: Symmetry and conservation law classification and exact solutions to the generalized KdV types of equations publication-title: Int. J. Bifur. Chaos – volume: 59 start-page: 497 year: 2010 end-page: 502 ident: CR13 article-title: Painlevé analysis. Lie symmetries, and exact solutions for the time-dependent coefficients Gardner equations publication-title: Nonlinear Dyn. doi: 10.1007/s11071-009-9556-2 – volume: 254 start-page: 2289 year: 2013 end-page: 2303 ident: CR16 article-title: Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2012.12.004 – year: 2002 ident: CR9 article-title: Symmetry and integration methods for differential equations publication-title: Applied Mathematical Sciences – volume: 44 start-page: 27 year: 1990 end-page: 53 ident: CR7 article-title: Painlevé analysis and the complete integrability of a generalized variable-coefficient Kadomtsev–Petviashvili equation publication-title: IMA J. Appl. Math. doi: 10.1093/imamat/44.1.27 – volume: 28 start-page: 299 year: 1980 end-page: 303 ident: CR17 article-title: On the structure of sympletic operators and hereditary symmetries publication-title: Lett. Nuovo Cimento doi: 10.1007/BF02798794 – year: 1993 ident: CR8 article-title: Applications of Lie groups to differential equations publication-title: Graduate Texts in Mathematics – volume: 228 start-page: 1 year: 2009 ident: 1130_CR1 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2008.06.009 – volume: 22 start-page: 1 issue: 1250188 year: 2012 ident: 1130_CR14 publication-title: Int. J. Bifur. Chaos – volume: 29 start-page: 1 year: 1987 ident: 1130_CR5 publication-title: Physics D doi: 10.1016/0167-2789(87)90046-7 – volume: 28 start-page: 299 year: 1980 ident: 1130_CR17 publication-title: Lett. Nuovo Cimento doi: 10.1007/BF02798794 – volume: 3 start-page: 229 year: 1987 ident: 1130_CR19 publication-title: Inverse Probl. doi: 10.1088/0266-5611/3/2/008 – volume-title: Applied Mathematical Sciences year: 2002 ident: 1130_CR9 – volume: 71 start-page: 2126 year: 2009 ident: 1130_CR12 publication-title: Nonlinear Anal. TMA doi: 10.1016/j.na.2009.01.075 – volume: 44 start-page: 27 year: 1990 ident: 1130_CR7 publication-title: IMA J. Appl. Math. doi: 10.1093/imamat/44.1.27 – volume: 39 start-page: 77 year: 1989 ident: 1130_CR6 publication-title: Physics D doi: 10.1016/0167-2789(89)90040-7 – volume: 57 start-page: 737 year: 2012 ident: 1130_CR15 publication-title: Commun. Theor. Phys. doi: 10.1088/0253-6102/57/5/02 – volume-title: Handbook of Exact Solutions for Ordinary Differential Equations year: 2003 ident: 1130_CR21 – volume-title: The Painlevé Handbook year: 2008 ident: 1130_CR3 – volume: 12 start-page: 238 year: 1989 ident: 1130_CR18 publication-title: Acta Math. Appl. Sin. – volume: 42 start-page: 159 year: 2013 ident: 1130_CR2 publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-012-0633-1 – volume-title: Graduate Texts in Mathematics year: 1993 ident: 1130_CR8 – volume: 59 start-page: 497 year: 2010 ident: 1130_CR13 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-009-9556-2 – volume: 24 start-page: 522 year: 1983 ident: 1130_CR4 publication-title: J. Math. 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| Snippet | In this paper, the Painlevé analysis is performed on the physical form of the third-order Burgers’ equation, the Painlevé property and integrability... In this paper, the Painleve analysis is performed on the physical form of the third-order Burgers' equation, the Painleve property and integrability... |
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| Title | Painlevé Test, Generalized Symmetries, Bäcklund Transformations and Exact Solutions to the Third-Order Burgers’ Equations |
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