호남수학학술지 (Honam Mathematical Journal)

  • 제33권2호
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  • Pages.247-259
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  • 2011
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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NEW EXACT TRAVELLING WAVE SOLUTIONS OF SOME NONLIN EAR EVOLUTION EQUATIONS BY THE(G'/G)-EXPANSION METHOD

  • Lee, You-Ho (Department of Internet Information, Daegu Hanny University) ;
  • Lee, Mi-Hye (Department of Mathematics, Sungkyunkwan University) ;
  • An, Jae-Young (Department of Mathematics, Sungkyunkwan University)
  • 투고 : 2011.04.15
  • 심사 : 2011.05.10
  • 발행 : 2011.06.25
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초록

In this paper, the $(\frac{G'}{G})$-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 $(\frac{G'}{G})$-expansion method is direct, concise, and effective, and can be applied to man other nonlinear evolution equations arising in mathematical physics.

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참고문헌

  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. https://doi.org/10.1143/PTP.53.419
  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. https://doi.org/10.1063/1.1666400
  5. F. Cariello, M, Tabor, Similarity reductions from extended Painleve' expansions for nonintegrable evolution equations, Physica D. 53(1991) 59-70. https://doi.org/10.1016/0167-2789(91)90164-5
  6. W. Malfliet, W. Hereman, The tanh method for travelling wave solutions of nonlinear equations, Phys. Scr. 54 (1996) 563-568. https://doi.org/10.1088/0031-8949/54/6/003
  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. https://doi.org/10.1016/j.chaos.2005.10.032
  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. https://doi.org/10.1016/j.amc.2006.07.002
  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. https://doi.org/10.1016/j.chaos.2005.05.016
  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. https://doi.org/10.1016/j.chaos.2005.05.016
  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. https://doi.org/10.1016/j.physleta.2005.05.085
  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. https://doi.org/10.1016/j.physleta.2006.03.081
  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. https://doi.org/10.1016/j.chaos.2005.10.009
  14. M.L. Wang, Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A 213 (1996) 279-287. https://doi.org/10.1016/0375-9601(96)00103-X
  15. A.M. Wazwaz, Distinct variants of the KdV equation with compact and non-compact structures, Appl. Math. Compt. 150 (2004) 365-377. https://doi.org/10.1016/S0096-3003(03)00238-8
  16. A.M. Wazwaz, Variants of the generalized KdV equations with compact and noncompact structures, Comput. Math. Appl. 47 (2004) 583-591. https://doi.org/10.1016/S0898-1221(04)90047-8
  17. X. Feng, Exploratory approach to explicit solution of nonlinear evolution equations, Int. J. Theor. Phys. 39 (2000) 207-222. https://doi.org/10.1023/A:1003615705115
  18. J.L. Hu, Explicit solutions to three nonlinear physical models, Phys. Lett. A 287 (2001) 81-89. https://doi.org/10.1016/S0375-9601(01)00461-3
  19. J.L. Hu, A new method of exact travelling wave solutions for coupled nonlinear differential equations, Phys. Lett. A 322 (2004) 211-216. https://doi.org/10.1016/j.physleta.2004.01.023
  20. J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals 30 (2006) 700-708. https://doi.org/10.1016/j.chaos.2006.03.020
  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. https://doi.org/10.1016/j.physleta.2007.07.051
  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. https://doi.org/10.1098/rsta.1972.0032
  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. https://doi.org/10.2991/jnmp.2006.13.4.12
  24. A. Bekir, New exact travelling wave solutions of some complex nonlinear equations, Commun. Nonlonear Sci. Numer. Simulat. 14(2009)1069-1077. https://doi.org/10.1016/j.cnsns.2008.05.007