Abstract
In this paper, we have presented the applicability of the first integral method for constructing exact solutions of (2+1)-dimensional Jaulent–Miodek equations. The first integral method is a powerful and effective method for solving nonlinear partial differential equations which can be applied to nonintegrable as well as integrable equations. The present paper confirms the significant features of the method employed and exact kink and soliton solutions are constructed through the established first integrals.
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References
V O Vakhnenko, E J Parkes and A J Morrison, Chaos, Solitons and Fractals 17(4), 683 (2003)
R Hirota, Phys. Rev. Lett. 27, 1192 (1971)
R Hirota, The direct method in soliton theory (Cambridge University Press, 2004)
W X Ma, Phys. Lett. A 180, 221 (1993)
W Malfliet, Am. J. Phys. 60(7), 650 (1992)
S A El-Wakil and M A Abdou, Chaos, Solitons and Fractals 31(4), 840 (2007)
E Fan, Phys. Lett. A 277, 212 (2000)
A M Wazwaz, Appl. Math. Comput. 187, 1131 (2007)
N A Kudryashov, Phys. Lett. A 342(12), 99 (2005)
N A Kudryashov, Chaos, Solitons and Fractals 24(5), 1217 (2005)
M Eslami, M Mirzazadeh and A Biswas, J. Mod. Opt. 60(19), 1627 (2013)
N K Vitanov, Z I Dimitrova and H Kantz, Appl. Math. Comput. 216(9), 2587 (2010)
W X Ma, T W Huang and Y Zhang, Phys. Scr. 82, 065003 (2010)
W X Ma and J-H Lee, Chaos, Solitons and Fractals 42, 1356 (2009)
M Eslami, A Neyrame and M Ebrahimi, J. King Saudi Univ. Sci. 24(1), 69 (2012)
Z S Feng and X H Wang, Phys. Lett. A 308, 173 (2003)
B Lu, Commun. Non. Sci. Numer. Simul. 17, 4626 (2012)
B Lu, J. Math. Anal. Appl. 395(2), 684 (2012)
B Lu, H Q Zhang and F D Xie, Appl. Math. Comput. 216, 1329 (2010)
A Biswas, M Mirzazadeh and M Eslami, Acta Phys. Polon. B 45(4), 849 (2014)
M Eslami, B Fathi Vajargah, M Mirzazadeh and A Biswas, Indian J. Phys. 88(2), 177 (2014)
M F El-Sabbagh and S I El-Ganaini, Appl. Math. Sci. 6(78), 3893 (2012)
H Jafari, A Sooraki, Y Talebi and A Biswas, Nonlinear Analysis: Modelling and Control. 17(2), 182 (2012)
X G Geng, C W Cao and H H Dai, J. Phys. A: Math. Gen. 34, 989 (2001)
M Jaulent and I Miodek, Lett. Math. Phys. 1(3), 243 (1976)
H Liu and F Yan, Int. J. Nonlinear Sci. 11, 200 (2011)
A M Wazwaz, Phys. Lett. A 373, 1844 (2009)
A M Wazwaz, Appl. Math. Lett. 25(11), 1936 (2012)
W X Ma and B Fuchssteiner, Int. J. Non-Linear Mech. 31, 329 (1996)
A Biswas and A H Kara, Appl. Math. Comput. 217(2), 944 (2010)
Acknowledgement
The authors are grateful to the anonymous referee for the careful checking of the details and for helpful comments that improved this paper.
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MATINFAR, M., ESLAMI, M. & ROSHANDEL, S. The first integral method to study the (2+1)-dimensional Jaulent–Miodek equations. Pramana - J Phys 85, 593–603 (2015). https://doi.org/10.1007/s12043-014-0916-1
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DOI: https://doi.org/10.1007/s12043-014-0916-1
Keywords
- (2+1)-dimensional Jaulent–Miodek equation
- the first integral method
- kinks
- solitons
PACS Nos
- 02.30.Jr
- 05.45.Yv