| GENERAL |
|
|
|
|
A Modification of Extended Homoclinic Test Approach to Solve the (3+1)-Dimensional Potential-YTSF Equation |
| M. T. Darvishi**, Mohammad Najafi
|
Department of Mathematics, Razi University, Kermanshah 67149, Iran
|
|
| Cite this article: |
|
M. T. Darvishi, Mohammad Najafi 2011 Chin. Phys. Lett. 28 040202 |
|
|
|
|
Abstract By means of the extended homoclinic test approach (EHTA) one can solve some nonlinear partial differential equations (NLPDEs) in their bilinear forms. When an NLPDE has no bilinear closed form we can not use this method. We modify the idea of EHTA to obtain some analytic solutions for the (3+1)-dimensional potential-Yu-Toda-Sasa-Fukuyama (YTSF) equation by obtaining a bilinear closed form for it. By comparison of this method and other analytic methods, like HAM, HTA and three-wave methods, we can see that the new idea is very easy and straightforward.
|
| Keywords:
02.30.Jr
02.70.Wz
|
|
|
Received: 16 July 2010
Published: 29 March 2011
|
|
| PACS: |
02.30.Jr
|
(Partial differential equations)
|
| |
02.70.Wz
|
(Symbolic computation (computer algebra))
|
|
|
|
|
|
[1] He J H 1999 Int. J. Non-Linear Mech. 34 699
[2] Darvishi M T, Khani F and Soliman A A 2007 Comput. Math. Appl. 54(7-8) 1055
[3] Darvishi M T and Khani F 2009 Chaos, Solitons and Fractals 39 2484
[4] Abbasbandy S and Darvishi M T 2005 Appl. Math. Comput. 163 1265
[5] Abbasbandy S and Darvishi M T 2005 Appl. Math. Comput. 170 95
[6] He J H 2006 Int. J. Mod. Phys. B 20 2561
[7] He J H 2005 Chaos, Solitons and Fractals 26 695
[8] He J H 2005 Int. J. Nonlinear Sci. Numer. Simul. 6 207
[9] Darvishi M T and Khani F 2008 Zeitschrift fur Naturforschung A 63 a19
[10] Darvishi M T, Khani F, Hamedi-Nezhad S and Ryu S W 2010 Int. J. Comput. Math. 87 908
[11] He J H 2001 Int. J. Nonlin. Sci. Numer. Simul. 2 257
[12] Darvishi M T, Karami A and Shin B C 2008 Phys. Lett. A 372 5381
[13] Shin B C, Darvishi M T and Karami A 2009 Int. J. Nonlin. Sci. Num. Simul. 10 137
[14] Darvishi M T 2004 Intl. J. Pure and Appl. Math. 1 419
[15] Darvishi M T, Kheybari S and Khani F 2006 Appl. Math. Comput. 182 98
[16] Darvishi M T and Javidi M 2006 Appl. Math. Comput. 173 421
[17] Darvishi M T, Khani F and Kheybari S 2007 Int. J. Comput. Math. 84 541
[18] Darvishi M T, Khani F and Kheybari S 2008 Nonlinear Sci. Numer. Simul. 13 2091
[19] Liao S J 1999 Int. J. Non-Linear Mech. 34 759
[20] Liao S J 2003 Beyond Perturbation: Introduction to the Homotopy Analysis Method (Boca Raton: Chapman & Hall/CRC Press)
[21] Liao S J 2004 Appl. Math. Comput. 147 499
[22] Liao S J 2005 Int. J. Heat Mass Transfer 48 2529
[23] Liao S J 2009 Commun. Nonlinear Sci. Numer. Simul. 14 2144
[24] Darvishi M T and Khani F 2009 Comput. Math. Appl. 58 360
[25] Aziz A, Khani F and Darvishi M T 2010 Zeitschrift fuer Naturforschung A 65 a 771
[26] He J H and Abdou M A 2007 Chaos, Solitons and Fractals 34 1421
[27] He J H and Wu X H 2006 Chaos, Solitons and Fractals 30 700
[28] He J H and Wu X H 2006 Chaos, Solitons and Fractals 29 108
[29] Khani F, Hamedi-Nezhad S, Darvishi M T and Ryu S W 2009 Nonlin. Anal.: Real World Appl. 10 1904
[30] Shin B C, Darvishi M T and Barati A 2009 Comput. Math. Appl. 58 2147
[31] Wu X H and He J H 2008 Chaos, Solitons and Fractals 38 903
[32] Dai Z D, Lin S Q, Li D L and Mu G 2010 Nonl. Sci. Lett. A 1 77
[33] Wang C J, Dai Z D and Liang L 2010 Appl. Math. Comput. 216 501
[34] Yu S J, Toda K, Sasa N and Fukuyama T 1998 J. Phys. A: Math. Gen. 31 3337
[35] Yan Z 2003 Phys. Lett. A 318 78
[36] Zhao Z H, Dai Z D and Han S 2010 Appl. Math. Comput. 217 4306
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
