New generalized hyperbolic functions and auto-Bäcklund transformation to find new exact solutions of the ( 2 + 1 ) -dimensional NNV equation
In the present Letter, we first time define new functions (called generalized hyperbolic functions) and devise new kinds of transformation (called generalized hyperbolic function transformation) to construct new exact solutions of nonlinear partial differential equations. Based on the generalized hy...
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| Published in: | Physics letters. A Vol. 357; no. 6; pp. 438 - 448 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
25.09.2006
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| ISSN: | 0375-9601, 1873-2429 |
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| Abstract | In the present Letter, we first time define new functions (called generalized hyperbolic functions) and devise new kinds of transformation (called generalized hyperbolic function transformation) to construct new exact solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation and the auto-Bäcklund transformation of the (
2
+
1
)-dimensional Nizhnik–Novikov–Veselov (NNV) equations, we obtain abundant families of new exact solutions of the NNV equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions and different regions of the independent variables in these solutions by their figures. As a result, we find that these parameter values and the region size of the independent variables affect some solution structure. Therefore, we may regulate these parameter values and the region size to control the shape and number of solitons on the basis of our different requirements by means of computer simulation. These solutions may be useful to explain some physical phenomena. |
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| AbstractList | In the present Letter, we first time define new functions (called generalized hyperbolic functions) and devise new kinds of transformation (called generalized hyperbolic function transformation) to construct new exact solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation and the auto-Bäcklund transformation of the (
2
+
1
)-dimensional Nizhnik–Novikov–Veselov (NNV) equations, we obtain abundant families of new exact solutions of the NNV equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions and different regions of the independent variables in these solutions by their figures. As a result, we find that these parameter values and the region size of the independent variables affect some solution structure. Therefore, we may regulate these parameter values and the region size to control the shape and number of solitons on the basis of our different requirements by means of computer simulation. These solutions may be useful to explain some physical phenomena. |
| Author | Ren, Yujie Zhang, Hongqing |
| Author_xml | – sequence: 1 givenname: Yujie surname: Ren fullname: Ren, Yujie email: ryj195535@163.com organization: Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China – sequence: 2 givenname: Hongqing surname: Zhang fullname: Zhang, Hongqing organization: Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China |
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| Keywords | ( 2 + 1 )-dimensional NNV equations Generalized hyperbolic functions Auto-Bäcklund transformation Exact solution Generalized hyperbolic function transformation |
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| References | Wang, Wang, Zhou (bib006) 2002; 303 Miura (bib003) 1978 Vekslerchik (bib005) 2004; 37 Konno, Wadati (bib002) 1975; 53 Ren, Zhand (bib008) 2006; 27 Lou (bib010) 2000; 277 Wang, Zhang (bib011) 2005; 16 Zhang, Chen (bib015) 2005; 23 Hu (bib009) 1994; 27 Veselov, Novikov (bib007) 1984; 30 Yan, Zhang (bib012) 2001; 34 Wadati (bib001) 1975; 38 Yan (bib013) 2003; 326 Wang, Wang (bib004) 2001; 287 Yan (bib014) 2004; 37 Konno (10.1016/j.physleta.2006.04.082_bib002) 1975; 53 Wang (10.1016/j.physleta.2006.04.082_bib004) 2001; 287 Yan (10.1016/j.physleta.2006.04.082_bib014) 2004; 37 Zhang (10.1016/j.physleta.2006.04.082_bib015) 2005; 23 Miura (10.1016/j.physleta.2006.04.082_bib003) 1978 Wang (10.1016/j.physleta.2006.04.082_bib006) 2002; 303 Wang (10.1016/j.physleta.2006.04.082_bib011) 2005; 16 Yan (10.1016/j.physleta.2006.04.082_bib012) 2001; 34 Hu (10.1016/j.physleta.2006.04.082_bib009) 1994; 27 Wadati (10.1016/j.physleta.2006.04.082_bib001) 1975; 38 Veselov (10.1016/j.physleta.2006.04.082_bib007) 1984; 30 Ren (10.1016/j.physleta.2006.04.082_bib008) 2006; 27 Vekslerchik (10.1016/j.physleta.2006.04.082_bib005) 2004; 37 Lou (10.1016/j.physleta.2006.04.082_bib010) 2000; 277 Yan (10.1016/j.physleta.2006.04.082_bib013) 2003; 326 |
| References_xml | – volume: 303 start-page: 45 year: 2002 ident: bib006 publication-title: Phys. Lett. A – volume: 27 start-page: 1331 year: 1994 ident: bib009 publication-title: J. Phys. A: Math. Gen. – volume: 16 start-page: 3 year: 2005 ident: bib011 publication-title: J. Mod. Phys. C – volume: 37 start-page: 5667 year: 2004 ident: bib005 publication-title: J. Phys. A: Math. Gen. – volume: 27 start-page: 959 year: 2006 ident: bib008 publication-title: Chaos Solitons Fractals – volume: 37 start-page: 841 year: 2004 ident: bib014 publication-title: J. Phys. A: Math. Gen. – volume: 326 start-page: 344 year: 2003 ident: bib013 publication-title: Physica A – volume: 23 start-page: 175 year: 2005 ident: bib015 publication-title: Chaos Solitons Fractals – volume: 53 start-page: 1652 year: 1975 ident: bib002 publication-title: Prog. Theor. Phys. – volume: 38 start-page: 681 year: 1975 ident: bib001 publication-title: J. Phys. Soc. Jpn. – volume: 34 start-page: 365 year: 2001 ident: bib012 publication-title: Commun. Theor. Phys. – volume: 287 start-page: 211 year: 2001 ident: bib004 publication-title: Phys. Lett. A – volume: 30 start-page: 588 year: 1984 ident: bib007 publication-title: Sov. Math. Dokl. – volume: 277 start-page: 94 year: 2000 ident: bib010 publication-title: Phys. Lett. A – year: 1978 ident: bib003 article-title: Bäcklund Transformation – volume: 326 start-page: 344 year: 2003 ident: 10.1016/j.physleta.2006.04.082_bib013 publication-title: Physica A doi: 10.1016/S0378-4371(03)00361-3 – volume: 38 start-page: 681 year: 1975 ident: 10.1016/j.physleta.2006.04.082_bib001 publication-title: J. Phys. Soc. Jpn. doi: 10.1143/JPSJ.38.681 – volume: 287 start-page: 211 year: 2001 ident: 10.1016/j.physleta.2006.04.082_bib004 publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(01)00487-X – volume: 303 start-page: 45 year: 2002 ident: 10.1016/j.physleta.2006.04.082_bib006 publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(02)00975-1 – volume: 37 start-page: 841 year: 2004 ident: 10.1016/j.physleta.2006.04.082_bib014 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/37/3/020 – volume: 27 start-page: 959 year: 2006 ident: 10.1016/j.physleta.2006.04.082_bib008 publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2005.04.063 – volume: 34 start-page: 365 year: 2001 ident: 10.1016/j.physleta.2006.04.082_bib012 publication-title: Commun. Theor. Phys. – year: 1978 ident: 10.1016/j.physleta.2006.04.082_bib003 – volume: 23 start-page: 175 year: 2005 ident: 10.1016/j.physleta.2006.04.082_bib015 publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2004.04.006 – volume: 16 start-page: 3 year: 2005 ident: 10.1016/j.physleta.2006.04.082_bib011 publication-title: J. Mod. Phys. C – volume: 53 start-page: 1652 year: 1975 ident: 10.1016/j.physleta.2006.04.082_bib002 publication-title: Prog. Theor. Phys. doi: 10.1143/PTP.53.1652 – volume: 30 start-page: 588 year: 1984 ident: 10.1016/j.physleta.2006.04.082_bib007 publication-title: Sov. Math. Dokl. – volume: 37 start-page: 5667 year: 2004 ident: 10.1016/j.physleta.2006.04.082_bib005 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/37/21/012 – volume: 27 start-page: 1331 year: 1994 ident: 10.1016/j.physleta.2006.04.082_bib009 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/27/4/026 – volume: 277 start-page: 94 year: 2000 ident: 10.1016/j.physleta.2006.04.082_bib010 publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(00)00699-X |
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| SubjectTerms | ( [formula omitted])-dimensional NNV equations Auto-Bäcklund transformation Exact solution Generalized hyperbolic function transformation Generalized hyperbolic functions |
| Title | New generalized hyperbolic functions and auto-Bäcklund transformation to find new exact solutions of the ( 2 + 1 ) -dimensional NNV equation |
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