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Further improved F-expansion method and new exact solutions of Konopelchenko–Dubrovsky equation. (English) Zbl 1083.35122

Summary: With the aid of the symbolic computation we improve the extended F-expansion method by J. Liu and K. Yang [Chaos Solitons Fractals 28, 111–121 (2004; Zbl 1062.35105)] and propose the further improved F-expansion method. Using this method, we get many exact solutions include Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions and so on.

MSC:

35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Citations:

Zbl 1062.35105
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References:

[1] Liu, Jb.; Yang, Kq., Chaos, Solitons & Fractals, 22, 111 (2004) · Zbl 1062.35105
[2] Ablowitz, M. J.; Segur, H., Soliton and the inverse scattering transformation (1981), SIAM: SIAM Philadelphia, PA · Zbl 0299.35076
[3] Wadati, M., J Phys Soc Jpn, 38, 673 (1975) · Zbl 1334.82022
[4] Wadati, M., J Phys Soc Jpn, 38, 681 (1975) · Zbl 1334.82023
[5] Konno, K.; Wadati, M., Prog Theor Phys, 53, 1652 (1975) · Zbl 1079.35505
[6] Miura, M. R., Backlund transformation (1978), Springer: Springer Berlin
[7] Matveev, V. B.; Salle, M. A., Darboux transformation and solitons (1991), Springer: Springer Berlin · Zbl 0744.35045
[8] Esteevez, P. G., J Math Phys, 40, 1406 (1999) · Zbl 0943.35078
[9] Dubrousky, V. G.; Konop, B. G., J Phys A, 27, 4619 (1994)
[10] Hirota, R. S., J Phys Lett A, 85, 407 (1981)
[11] Tam, H. W.; Ma, W. X.; Hu, X. B.; Wang, D. L., J Phys Soc Jpn, 69, 45 (2000) · Zbl 0965.35144
[12] Novikov, D. P., Math J, 40, 136 (1999)
[13] Cao, C. W.; Geng, X. G.; Wang, H. Y., J Math Phys, 43, 621 (2002) · Zbl 1052.37050
[14] Malfliet, W., Am J Phys, 60, 650 (1992) · Zbl 1219.35246
[15] Yan, C. T., Phys Lett A, 224, 77 (1996) · Zbl 1037.35504
[16] Xia, T-c.; Lü, Z-s.; Zhang, H-q., Chaos, Solitons & Fractals, 20, 561 (2004) · Zbl 1049.35171
[17] Yan, Zh.y, Chaos, Solitons & Fractals, 18, 299 (2003) · Zbl 1069.37060
[18] Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q., Phys Lett A, 289, 69 (2001) · Zbl 0972.35062
[19] Fu, Z. T.; Liu, S. K.; Liu, S. D.; Zhao, Q., Phys Lett A, 290, 72 (2001) · Zbl 0977.35094
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