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NEW EXACT TRAVELLING WAVE SOLUTIONS OF SOME NONLIN EAR EVOLUTION EQUATIONS BY THE(G`/G)-EXPANSION METHOD
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  • Journal title : Honam Mathematical Journal
  • Volume 33, Issue 2,  2011, pp.247-259
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2011.33.2.247
 Title & Authors
NEW EXACT TRAVELLING WAVE SOLUTIONS OF SOME NONLIN EAR EVOLUTION EQUATIONS BY THE(G`/G)-EXPANSION METHOD
Lee, You-Ho; Lee, Mi-Hye; An, Jae-Young;
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 Abstract
In this paper, the -expansion method is used to construct new exact travelling wave solutions of some nonlinear evolution equations. The travelling wave solutions in general form are expressed by the hyperbolic functions, the trigonometric functions and the rational functions, as a result many previously known solitary waves are recovered as special cases. The -expansion method is direct, concise, and effective, and can be applied to man other nonlinear evolution equations arising in mathematical physics.
 Keywords
-expansion method;Homogeneous balance;Travelling wave solutions;Solitary wave solutions;BBM equation;Weak symmetric equation;Mindlin equation;Higgs equations;
 Language
English
 Cited by
 References
1.
M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform, Cambride Univ. Press, Cambridge, 1991.

2.
M. Wadati, H. Shanuki, K. Konno, Relationships among inverse method, Back-lund transformation and an infinite number of conservative laws, Prog. Theor. Phys. 53 (1975) 419-436. crossref(new window)

3.
V.A. Matveev, M.A. Salle, Darboux Transformation and Solitons, Springer, Berlin, 1991.

4.
R. Hirota, Exact N-soliton solutions of the wave equation of long waves in shallow water and in nonlinear lattices, J. Math. Phys. 14 (1973) 810. crossref(new window)

5.
F. Cariello, M, Tabor, Similarity reductions from extended Painleve' expansions for nonintegrable evolution equations, Physica D. 53(1991) 59-70. crossref(new window)

6.
W. Malfliet, W. Hereman, The tanh method for travelling wave solutions of nonlinear equations, Phys. Scr. 54 (1996) 563-568. crossref(new window)

7.
S. A. El-Wakil, M.A. Abdou, New exact travelling wave solutions using modified extended tanh-function method, Chaos Solitons Fractals 31(4) (2007) 840-852. crossref(new window)

8.
A. M. Wazwaz, The extended tanh method for new solitions solutions for many forms of the fifth-order KdV equations, Appl. Math.Comput. 184(2) (2007) 1002-1014. crossref(new window)

9.
C. Q. Dai, J.F. Zhang, Improved Jacob-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system, Chaos Solitons Fractals 28 (2006)112-126. crossref(new window)

10.
X. Q. Zhao, H. Y. Zhi, H. Q. Zhang, Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system, Chaos Solitons Fractals 28 (2006) 112-126. crossref(new window)

11.
M.L. Wang, X.Z. Li, Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations, Phys. Lett. A 343 (2005) 48-54. crossref(new window)

12.
J.L.Zhang, M.L. Wang, X.Z.Li, The subsidiary ordinary differential equations and the exact solutions of the higher order dispersive nonlinear Schrodinger equation. Phys. Lett. A 357 (2006) 188-195. crossref(new window)

13.
M.L. Wang, X.Z. Li, J.L.Zhang, Various exact solutions of nonlinear Schrodinger equation with two nonlinear terms, Chaos Solitons Fractals 31 (2007) 594-601. crossref(new window)

14.
M.L. Wang, Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A 213 (1996) 279-287. crossref(new window)

15.
A.M. Wazwaz, Distinct variants of the KdV equation with compact and non-compact structures, Appl. Math. Compt. 150 (2004) 365-377. crossref(new window)

16.
A.M. Wazwaz, Variants of the generalized KdV equations with compact and noncompact structures, Comput. Math. Appl. 47 (2004) 583-591. crossref(new window)

17.
X. Feng, Exploratory approach to explicit solution of nonlinear evolution equations, Int. J. Theor. Phys. 39 (2000) 207-222. crossref(new window)

18.
J.L. Hu, Explicit solutions to three nonlinear physical models, Phys. Lett. A 287 (2001) 81-89. crossref(new window)

19.
J.L. Hu, A new method of exact travelling wave solutions for coupled nonlinear differential equations, Phys. Lett. A 322 (2004) 211-216. crossref(new window)

20.
J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals 30 (2006) 700-708. crossref(new window)

21.
M.L. Wang, X. Li, J. Zhang, The ($\frac{G'}{G}$)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A 372 (2008) 417-423. crossref(new window)

22.
T.B. Benjamin, J.L. Bona, J.J. Mahony, Model equation for long waves in nolinear dispersive system, Philos. Trans. Royal. Soc. Lond. Ser. A 272(1972)47-78. crossref(new window)

23.
B. Abraham-Shrauner, K.S. govinder, Provenance of Type ll hidden symmeries from nonlinear partial differential equations, J. Nonlinear Math. Phys. 13(2006)612-622. crossref(new window)

24.
A. Bekir, New exact travelling wave solutions of some complex nonlinear equations, Commun. Nonlonear Sci. Numer. Simulat. 14(2009)1069-1077. crossref(new window)