Lie symmetry analysis and exact solutions of (3+1) dimensional Yu–Toda–Sasa–Fukuyama equation in mathematical physics
In this paper, the Lie symmetry analysis method has been proposed for finding similarity reduction and exact solutions of nonlinear evolution equation. Here for illustrating the effectiveness and accuracy of proposed method, we have taken (3+1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation. Also...
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| Published in | Computers & mathematics with applications (1987) Vol. 73; no. 2; pp. 253 - 260 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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15.01.2017
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| Abstract | In this paper, the Lie symmetry analysis method has been proposed for finding similarity reduction and exact solutions of nonlinear evolution equation. Here for illustrating the effectiveness and accuracy of proposed method, we have taken (3+1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation. Also by using symmetry reduction method, we have reduced nonlinear partial differential equation (NPDE) to nonlinear ordinary differential equation, which has advantage to provide semi analytical solution. We have obtained infinitesimal generators, the entire geometric vector field, commutator table of Lie algebra and symmetry group by using Lie symmetry analysis method. Then, we have used tanh method for finding new analytical exact solutions of some reduced transform equations. |
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| AbstractList | In this paper, the Lie symmetry analysis method has been proposed for finding similarity reduction and exact solutions of nonlinear evolution equation. Here for illustrating the effectiveness and accuracy of proposed method, we have taken (3+1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation. Also by using symmetry reduction method, we have reduced nonlinear partial differential equation (NPDE) to nonlinear ordinary differential equation, which has advantage to provide semi analytical solution. We have obtained infinitesimal generators, the entire geometric vector field, commutator table of Lie algebra and symmetry group by using Lie symmetry analysis method. Then, we have used tanh method for finding new analytical exact solutions of some reduced transform equations. |
| Author | Saha Ray, S. Sahoo, S. |
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| Cites_doi | 10.1088/1742-6596/96/1/012186 10.1016/j.chaos.2006.04.005 10.1016/S0034-4877(99)80166-9 10.1016/j.cam.2008.10.052 10.1016/j.chaos.2009.01.040 10.1016/j.camwa.2008.02.045 10.1088/0305-4470/31/14/018 10.1016/j.chaos.2004.09.122 10.1016/j.physleta.2003.08.073 10.1119/1.17120 10.1007/s10884-011-9228-z |
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| Keywords | (3+1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation Lie symmetries analysis method Infinitesimal generator Tanh method |
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| References | Yu, Toda, Sasa, Fukuyama (br000030) 1998; 31 Toda, Song, Fukuyama (br000035) 1999; 44 Olver (br000005) 1993 Wang (br000055) 2008; 96 Zhang, Xuan, Zhang, Wang (br000065) 2007; 34 Bluman, Cole (br000015) 1969; 18 Guo, Yu (br000060) 2011; 23 Borhanifar, Kabir (br000050) 2009; 229 Yan (br000070) 2003; 318 Lie (br000010) 1888 Wazwaz (br000075) 2005; 25 Boz, Bekir (br000025) 2008; 56 Wazwaz (br000045) 2008; 203 Malfliet (br000080) 1992; 60 Zeng, Dai, Li (br000020) 2009; 42 Schff (br000040) 1992 Zhang (10.1016/j.camwa.2016.11.016_br000065) 2007; 34 Wang (10.1016/j.camwa.2016.11.016_br000055) 2008; 96 Malfliet (10.1016/j.camwa.2016.11.016_br000080) 1992; 60 Yan (10.1016/j.camwa.2016.11.016_br000070) 2003; 318 Borhanifar (10.1016/j.camwa.2016.11.016_br000050) 2009; 229 Zeng (10.1016/j.camwa.2016.11.016_br000020) 2009; 42 Yu (10.1016/j.camwa.2016.11.016_br000030) 1998; 31 Toda (10.1016/j.camwa.2016.11.016_br000035) 1999; 44 Guo (10.1016/j.camwa.2016.11.016_br000060) 2011; 23 Wazwaz (10.1016/j.camwa.2016.11.016_br000075) 2005; 25 Schff (10.1016/j.camwa.2016.11.016_br000040) 1992 Olver (10.1016/j.camwa.2016.11.016_br000005) 1993 Boz (10.1016/j.camwa.2016.11.016_br000025) 2008; 56 Bluman (10.1016/j.camwa.2016.11.016_br000015) 1969; 18 Lie (10.1016/j.camwa.2016.11.016_br000010) 1888 Wazwaz (10.1016/j.camwa.2016.11.016_br000045) 2008; 203 |
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Comput. contributor: fullname: Wazwaz – volume: 25 start-page: 55 year: 2005 ident: 10.1016/j.camwa.2016.11.016_br000075 article-title: The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2004.09.122 contributor: fullname: Wazwaz – volume: 318 start-page: 78 year: 2003 ident: 10.1016/j.camwa.2016.11.016_br000070 article-title: New families of nontravelling wave solutions to a new (3 + 1)-dimensional potential-YTSF equation publication-title: Phys. Lett. A doi: 10.1016/j.physleta.2003.08.073 contributor: fullname: Yan – volume: 60 start-page: 650 year: 1992 ident: 10.1016/j.camwa.2016.11.016_br000080 article-title: Solitary wave solutions of nonlinear wave equations publication-title: Amer. J. 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| SubjectTerms | (3[formula omitted]1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation Exact solutions Generators Infinitesimal generator Lie groups Lie symmetries analysis method Mathematical analysis Mathematical models Nonlinear differential equations Nonlinear equations Nonlinear evolution equations Partial differential equations Reduction Studies Symmetry Tanh method |
| Title | Lie symmetry analysis and exact solutions of (3+1) dimensional Yu–Toda–Sasa–Fukuyama equation in mathematical physics |
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