Abstract
The (G′/G)-expansion method and its simplified version are used to obtain generalized travelling wave solutions of five nonlinear evolution equations (NLEEs) of physical importance, viz. the (2+1)-dimensional Maccari system, the Pochhammer–Chree equation, the Newell–Whitehead equation, the Fitzhugh–Nagumo equation and the Burger–Fisher equation. A variety of special solutions like periodic, kink–antikink solitons, bell-type solitons etc. can easily be derived from the general results. Three-dimensional profile plots of some of the solutions are also drawn.
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References
P G Drazin and R S Johnson, Solitons: An introduction (Cambridge University Press, Cambridge, 1989)
M J Ablowitz and P A Clarkson, Solitons, nonlinear evolution equations and inverse scattering transform (Cambridge University Press, Cambridge, 1990)
R Hirota, Direct method of finding exact solutions of nonlinear evoluton equations, in: Backlund transformations edited by R Bullough (World Scientific, Singapore, 1987)
H J Satzuma, in: Soliton theory and exact solvable nonlinear equations edited by M Ablowitz, B Fuchssteiner and M Kruskal (Springer, Berlin, 1980) p. 1157
F Cariello and M Tabor, Physica D39, 77 (1989)
W Hereman and M Takaoka, J. Phys. A23, 4805 (1990)
M Wang, Phys. Lett. A199, 169 (1995)
W Malfliet, Am. J. Phys. 60, 650 (1992)
W Malfliet and W Hereman, Phys. Scr. 54, 569 (1996)
A M Wazwaz, Pramana–J. Phys. 77, 233 (2011)
E Fan and H Zhang, Phys. Lett. A246, 403 (1998)
E Fan, Phys. Lett. A277, 212 (2000)
A M Wazwaz, Math. Comput. Model. 40, 499 (2004)
E Fan and Y C Hon, Appl. Math. Comput. 141, 351 (2003)
Z Fu and Q Zhao, Phys. Lett. A289, 69 (2001)
R S Kaushal, R Kumar and A Prasad, Pramana–J. Phys. 67, 249 (2006)
C Q Dai and J F Zhang, Chaos, Solitons and Fractals 27, 1042 (2006)
J H He and M A Abdou, Chaos, Solitons and Fractals 34, 1421 (2007)
M Wang, X Li and J Zhang, Phys. Lett. A372, 417 (2008)
J Zhang, X Wei and Y Lu, Phys. Lett. A372, 3653 (2008)
S Zhang, L Tong and W Wang, Phys. Lett. A372, 2254 (2008)
E M E Zayed and K A Gepreel, J. Math. Phys. 50, 013502 (2008)
D D Ganji and M Abdollahzadeh, J. Math. Phys. 50, 013519 (2009) B S Bahrami, H Abdollazadeh, I M Berizani, D D Gangi and M Abdollazadeh, Pramana–J. Phys. 77, 263 (2011)
T Ozis and I Aslan, Commun. Theor. Phys. 51, 577 (2009)
E M E Zayed and K A Gepreel, Int. J. Nonlin. Sci. 7, 501 (2009)
A Malik, F Chand and S C Mishra, Appl. Math. Comput. 216, 2596 (2010)
R M El-Shiekh, Int. J. Nonlin. Sci. 10, 212 (2010)
E M E Zayed, J. Phys. A: Math. Theor. 42, 195202 (2009)
S Guo and Y Zhou, Appl. Math. Comput. 215, 3214 (2010)
X Fan, S Yang and D Zhao, Int. J. Nonlin. Sci. 8, 368 (2009)
A Maccari, J. Math. Phys. 37, 6207 (1996)
H Zhao, Chaos, Solitons and Fractals 36, 359 (2008)
A Bekir, Commun. Nonlin. Sci. Numer. Simul. 14, 1069 (2009)
S Li-Na and Z H Qing, Commun. Theor. Phys. 44, 783 (2005)
P J Ting and G T Xun, Commun. Theor. Phys. 48, 7 (2007)
W Zhang and M Wenxiu, Appl. Math. Mech. 20, 666 (1999)
L Jibin and Z Lijun, Chaos, Solitons and Fractals 14, 581 (2002)
H S Rosu and O Cornejo-Perez, Phys. Rev. E71, 046607 (2005)
S M Allen and J W Cahn, Acta Metall. 27, 1085 (1979)
B Q Lu, B Z Xiu, Z L Pang and X F Jiang, Phys. Lett. A175, 113 (1993)
J Zhang, Int. J. Theor. Phys. 35, 1793 (1996)
A M Wazwaz, Appl. Math. Comput. 188, 1467 (2007)
W Xinyi and L Yuekai, Chin. Phys. Lett. 7, 144 (1990)
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MALIK, A., CHAND, F., KUMAR, H. et al. Exact solutions of some physical models using the (G′/G)-expansion method. Pramana - J Phys 78, 513–529 (2012). https://doi.org/10.1007/s12043-011-0253-6
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DOI: https://doi.org/10.1007/s12043-011-0253-6